Gr 10 Math June P1 Hard

Which set of numbers includes negative values?

What characterizes irrational numbers?

Which of the following is a property of rational numbers?

Which subset of real numbers includes the number zero?

Which of the following statements about real numbers is true?

Which of the following sets contains only non-real numbers?

Which property characterizes an irrational number?

What is the first step to convert a recurring decimal into a rational number?

Which of the following describes surds?

When rounding the number 3.476 to two decimal places, what is the resulting number?

What key component defines a rational number?

What distinguishes a terminating decimal from a repeating decimal?

Which method is used for estimating the value of a surd?

In the rounding process, what happens if the digit to be rounded up is a 9?

Which part of a mathematical expression represents the power to which a base is raised?

What is the maximum number of solutions for a quadratic equation?

Which step is NOT involved in solving a linear equation?

When solving simultaneous equations, what is the primary goal of substitution?

What should be done to ensure that a quadratic equation is solvable?

Which characteristic differentiates linear equations from quadratic equations?

Which of the following is crucial when solving any equation?

After factoring a quadratic equation to find its roots, what is the next step?

Which method is effective for eliminating a variable in simultaneous equations?

What are the potential outcomes of a quadratic equation?

In the method of solving linear equations, what is the purpose of grouping like terms?

What is the effect of increasing the value of the gradient, m, in the equation y = mx + c?

When solving linear inequalities, what must occur if both sides of the inequality are divided by a negative number?

In the context of literal equations, what does changing the subject of the formula involve?

What is required for graphically solving a system of simultaneous equations?

In the solving process of word problems, what is the first step to take after reading the problem?

When isolating the unknown variable in a literal equation, what must be considered?

What characteristic defines linear functions of the form y = mx + c?

What happens to the graph of a linear function when c is less than 0?

In solving equations, what represents the solution to the problem stated in a word problem?

What is a critical aspect to remember when taking the square root of both sides in an equation?

What is the result of multiplying the monomial 3 and the binomial (x + 4)?

Which expression correctly represents the product of the binomials (2x + 3) and (x + 5)?

Which of these is true about the factorization of the expression x^2 - 9?

What is the correct method to factor the trinomial 2x^2 + 8x + 6?

What is the sum of the cubes x^3 + 27 factored?

When simplifying the fraction $rac{x^2 - 4}{x^2 + 2x}$, what is the first step?

Which expression correctly describes the difference of cubes x^3 - y^3?

What does the expression (4x + 2)(x^2 + 3x - 2) yield when simplified?

Which of the following explains the process of factoring by grouping?

In the operation of dividing two fractions $rac{a}{b}$ and $rac{c}{d}$, which is the correct procedure?

What effect does a greater value of $a$ have on the graph of a parabola?

What is the domain of the tangent function defined in the content?

What is the result of simplifying the expression \( rac{a^5}{a^2} imes a^3 \ ?

How do you determine the vertical shift in the equation of a hyperbola?

In determining the equation of a parabola, what role does the y-intercept play?

Which law states that ( (ab)^n = a^n b^n )?

How can you express the square root of a as a rational exponent?

What is the significance of asymptotes in the context of hyperbolas?

How can the amplitude of a sine or cosine function be determined?

Which expression correctly applies the zero exponent rule?

What is the formula for calculating the points of intersection between two graphs?

When solving the equation ( 2^x = 8 ), which method is appropriate?

What will be the result of applying the laws of exponents to the expression ( a^{3/4} imes a^{1/2} )?

What information do the quadrants of a hyperbola provide when determining its equation?

Which of the following correctly exemplifies the law for negative exponents?

What method is used to solve for $a$ in the equation of a hyperbola?

What is the primary use of the distance formula in interpreting graphs?

To simplify ( \frac{a^4 b^2}{a^2 b} ), what is the first step?

In rational exponents, how do you express ( \sqrt[3]{x} )?

What is the range of the function if $a < 0$ in the form $f(x) = ax^2 + q$?

Which statement correctly describes the characteristics of hyperbolic functions in the form $y = \frac{a}{x} + q$?

For the hyperbolic function $y = \frac{a}{x} + q$, what is the equation of the horizontal asymptote?

If $a > 0$ in the function $y = ax^2 + q$, how is the graph described?

Which characteristics are true for the domain of the hyperbolic functions?

What can be said about the turning points of the function $f(x) = ax^2 + q$ when $a < 0$?

In the function $y = ab^x + q$, what is the sign of $a$ if the range is described as $, {f(x) > q}$?

What are the axes of symmetry for the hyperbolic function $y = \frac{a}{x} + q$?

What is the effect of $q$ on a hyperbolic graph with $q < 0$?

How do the signs of $a$ affect the graph of the function $y = \frac{a}{x} + q$?

How does the sign of the coefficient 'a' affect the graph of an exponential function of the form $y = ab^x + q$?

What is the effect of changing the value of 'b' in the exponential function $y = ab^x + q$?

For a sine function of the form $y = a ext{sin} heta + q$, what change occurs when $a < 0$?

Which statement correctly describes the range of the function $y = a ext{cos} heta + q$ when $a > 0$?

Which of the following points represent the maximum turning point of the sine function $y = ext{sin} heta$?

What is the horizontal asymptote of the exponential function $y = ab^x + q$?

What happens to the graph of the function $y = a ext{tan} heta + q$ if $q < 0$?

How does the transformation $y = 2 ext{sin} heta + 1$ affect the sine wave?

For the tangent function $y = an heta$, where are the vertical asymptotes located?

What defines the period of the sine and cosine functions?

What is the relationship between the sign of the coefficient $a$ and the shape of the parabolic graph?

How does the value of $q$ influence the graph of the equation $y = ax^2 + q$?

For the linear equation $y = mx + c$, what does the y-intercept represent?

Which statement correctly defines the range of the function $f(x) = mx + c$?

What is the effect of increasing the absolute value of $a$ in the equation $y = ax^2 + q$?

When sketching a straight-line graph, which two points can be used effectively?

If the coefficient $m$ is negative in the equation $y = mx + c$, what type of slope does the line have?

Which of the following explains why the domain of $f(x) = mx + c$ is all real numbers?

If $q < 0$ in the quadratic function $y = ax^2 + q$, where does the vertex lie in relation to the x-axis?

Which of the following numbers is classified as an irrational number?

Which set of numbers includes only whole numbers?

What defines a rational number?

Which of the following is NOT a subset of rational numbers?

What is the primary characteristic of integers?

What foundational property applies to the set of real numbers?

What is the defining feature of irrational numbers compared to rational numbers?

Which statement is true about terminating decimals?

When estimating the value of a surd, what is the first step?

Which of the following is a correct characteristic of surds?

In the rounding process, what occurs if the digit to be rounded up is 9?

Which process is used to convert a recurring decimal into a rational number?

How are rational numbers classified in terms of their decimal representation?

What role does the coefficient play in a mathematical expression?

Which of these represents a defining characteristic of rational numbers?

What is the maximum number of solutions for a linear equation?

When solving a quadratic equation, what form must it be in?

Which of the following strategies is NOT a method for solving simultaneous equations?

What should be done first when checking solutions for a quadratic equation?

What is the implication of balancing an equation when solving?

Which statement about the nature of roots in a quadratic equation is accurate?

In the method of solving linear equations, what does isolating the variable accomplish?

Which method effectively reduces the complexity in solving simultaneous equations?

When factorizing a quadratic equation in the form $ax^2 + bx + c = 0$, what must be ensured?

What is the result of multiplying the expression ( (3x + 2)(x + 5) )?

What expression represents the factorization of the quadratic trinomial ( 2x^2 + 7x + 3 )?

Using the identity for the difference of two squares, how would you factor ( 16x^2 - 25 )?

What is the first step required when simplifying the fraction ( \frac{2x^2 - 8}{2x} )?

When using the method of factorising by grouping, what is the purpose of grouping terms?

What is the final form of the difference of cubes ( x^3 - 8 ) when fully factored?

What is a key difference in simplifying the expression ( \frac{a^2 - b^2}{a + b} ) as opposed to ( a + b )?

To simplify the algebraic fraction ( \frac{x^2 + 4x + 4}{x + 2} ), what process must be applied first?

What does the following multiplication yield: ( a(b + c) + d(b + c) )?

What is the range of the function given that the coefficient $a$ is negative?

Which of the following describes the turning point of the function when $a$ is greater than zero?

What characterizes the domain of the function $y = rac{a}{x} + q$?

What will happen to the graph of $y = rac{a}{x} + q$ if $q$ is set to zero?

How is the x-intercept of the hyperbolic function $y = rac{a}{x} + q$ determined?

Which of the following statements about the axis of symmetry for the function $f(x) = ax^2 + q$ is true?

For the exponential function $y = ab^x + q$, what can be inferred if $a$ is less than zero?

What determines if the hyperbolic graph lies in the first and third quadrants?

What determines the slope of the graph in the linear equation $y = mx + c$?

What is true about the y-intercept of the hyperbolic function $y = rac{a}{x} + q$?

Which of the following statements about solving linear inequalities is true?

What is the primary goal of the problem-solving strategy in word problems?

What happens to the graph of a linear equation if $c$ is increased?

In the context of literal equations, what does isolating the unknown variable involve?

What should be done if the unknown variable in a literal equation appears in more than one term?

What is a key difference between solving graphical systems of equations and algebraic methods?

When solving word problems, what is the process to write the equations?

Why is it important to check the solution after solving an equation?

In the process of solving simultaneous equations graphically, what represents the solution?

What is the effect on the shape of the parabola when the value of $a$ in the equation $y = ax^2 + q$ is greater than 1?

If the y-intercept of a linear function is given by the equation $y = mx + c$ as $c = -4$, which of these statements is correct?

In the equation of a straight line $y = mx + c$, what can be inferred if both $m$ and $c$ are equal to zero?

How does changing $q$ from positive to negative in the quadratic function $y = ax^2 + q$ affect the graph?

What do the signs of $m$ and $c$ indicate about the straight line in the equation $y = mx + c$ when both are positive?

In a typical function $f(x) = mx + c$, if $m < 0$, what characteristic can be expected from the graph?

For the quadratic function $y = ax^2 + q$, what structure does the graph take if $a$ is negative and $q$ is positive?

For an exponential function of the form $y = ab^x + q$, if $a < 0$ and $b > 1$, how does the graph behave?

In the context of linear equations, what is the primary interpretation of the gradient $m$?

Which characteristic best describes the range of a sine function $y = a ext{sin} heta + q$ when $|a| > 1$?

What results from the inequality $c < 0$ when analyzing the properties of the line $y = mx + c$?

In the graph of the function $y = a ext{cos} heta + q$, what does the value of $a < 0$ imply about the amplitude?

Which statement accurately describes the behavior of the function $y = a an heta + q$ regarding its vertical shifts?

Which statement is valid for the range of the function $f(x) = ax^2 + q$ when $a > 0$?

What happens to the horizontal asymptote of an exponential function $y = ab^x + q$ when $q < 0$?

When sketching the graph of $y = a ext{sin} heta + q$, how does an amplitude of $|a| < 1$ affect the graph?

In the context of trigonometric function transformations, what does a positive value of $q$ do to the cosine graph?

How does the decay of a function of the form $y = ab^x + q$ manifest when $0 < b < 1$?

What is the impact on the function $y = a ext{tan} heta + q$ if $|a| > 1$?

When simplifying the expression $\frac{a^5}{a^2} \times a^3$, what is the correct final result?

For the exponential equation $2^x = 8$, what method would effectively lead to finding the value of x?

In the expression $(ab)^{m/n}$, how can this be further simplified according to the exponent laws?

What is the result when applying the negative exponent law to the term $a^{-3}$?

How would you correctly express the product $a^{1/2} \times a^{2/3}$?

Which method is NOT correct for simplifying an exponential expression?

What is the result of the expression $(x^3y^{-2})^2$ when simplified?

Which of the following represents the process of solving the exponential equation $3^x = 27$?

What is the equivalent expression for $rac{a^{1/3}}{a^{1/2}}$?

When expressing the roots of an expression with a fractional exponent, like $\sqrt[4]{x}$, what is its fractional equivalent?

What is the y-intercept of the tangent function when expressed in the form $y = a \tan \theta + q$?

How can you determine the direction and width of a parabola given the equation $y = ax^2 + q$?

In determining the equation of a hyperbola, what does the value of $q$ affect?

Which of the following correctly identifies the asymptotes of the function $y = \frac{a}{x} + q$?

What is the significance of the points where $\theta = 90°$ and $\theta = 270°$ for the tangent function?

To determine the equation of a trigonometric function, which of the following methods should NOT be used?

What can be deduced about the domain of the function given by $y = a \tan \theta + q$?

In interpreting the graphs of parabolas, what is the necessary action to find the x-intercepts?

How does changing the value of $a$ in the equation of a hyperbola $y = \frac{a}{x} + q$ affect the graph?

Which of the following statements correctly describes a characteristic of natural numbers?

What best defines the set of integers?

Which of the following numbers is classified as an irrational number?

In which scenario would a number not belong to the set of rational numbers?

What distinguishes whole numbers from natural numbers?

Which set correctly represents real numbers?

What is a correct characteristic of irrational numbers?

Which type of decimal can be classified as rational?

How can the square root of a number be classified in terms of its properties?

What is the process involved in converting a terminating decimal into a rational number?

What step is essential when estimating the value of a surd?

What happens during the rounding process if the digit after the place you are rounding is a 5?

When comparing the decimal expansions of rational and irrational numbers, which statement is true?

Which of the following is NOT true about surds?

To convert a recurring decimal into a rational number, which method is employed?

What is the effect of increasing the gradient, $m$, in the equation $y = mx + c$?

What is the result when multiplying the binomial (2x + 3) by the binomial (x + 5)?

When solving linear inequalities, which of the following statements is true if one side is divided by a negative number?

In the context of literal equations, what does 'changing the subject of the formula' entail?

Which identity correctly factors the expression x^3 - 64?

What expression represents the product of a monomial 'a' and the binomial (x + y)?

What is the first step in solving word problems using equations?

How is the solution to a system of simultaneous equations represented graphically?

What is the first step when simplifying the fraction ( \frac{x^2 - 4}{x^2 + 2x} )?

Which method is crucial for isolating an unknown variable in a literal equation?

What is the correct result of using the identity for the sum of two cubes on the expression x^3 + 125?

Which method can be used to factor the expression x^2 + 5x + 6?

What happens to the graph of a linear function when the y-intercept, $c$, is negative?

When substituting into one of the original equations after using elimination, what is the goal?

When multiplying the expression (3x + 4) by the trinomial (2x + 5 + 1), which term results from the expansion?

What does the expression ( \frac{a^5}{a^2} \cdot a^3 ) simplify to?

Which principle must be remembered when taking the square root of both sides of an equation?

What is an essential characteristic of linear functions of the form $y = mx + c$?

Which of the following describes a common method used for factorization of quadratic expressions?

In arriving at the expression ( (x + 2)(x - 2) ), what type of factorization is employed?

What expression results from applying the negative exponent law to $a^{-3}$?

When simplifying the expression $\frac{a^5}{a^2 \times a^{-3}}$, what is the final result?

Which of the following correctly describes the simplification of the expression $(2x^3y^{-2})^2$?

What is the value of $\left(\frac{a^3}{b^2}\right)^{2/3}$ when applying the exponent rules?

If $\frac{2^{3/n}}{2^{1/n}}$ is simplified, what is the result?

Which equation correctly represents the law of exponents for the expression $(x^2y^{-3})^{3}$?

What is the result of simplifying the expression $a^0 \cdot b^0$?

When using logarithms to solve the equation $2^x = 16$, which step should be taken first?

What is the outcome of simplifying the expression $\frac{(x^4y^{-2})^2}{x^{-2}y}$?

What describes the turning point of the graph when the coefficient a is less than zero?

For the function of the form y = ax^2 + q, what determines the direction of the parabolic graph?

What is the behavior of y = (a/x) + q as x approaches zero?

How is the range of the function y = ax^2 + q determined if a is greater than zero?

When a hyperbolic function y = (a/x) + q has q greater than zero, what is the vertical shift of the graph?

What conditions must be met for a hyperbolic function to have no x-intercept?

In an exponential function represented as y = ab^x + q, which factor affects the growth direction of the graph?

What is the horizontal asymptote for a hyperbolic function of the form y = (a/x) + q?

The axis of symmetry for the function of the form f(x) = ax^2 + q is defined as:

How does changing the sign of the coefficient 'a' in the equation of a parabola affect its orientation?

What is the significance of the y-intercept 'c' in the linear equation y = mx + c?

What can be inferred about a parabola when 'q' equals zero in the equation y = ax^2 + q?

For a linear equation with a gradient of m = 0, what can be said about the graph?

Which statement accurately describes the domain of the function f(x) = mx + c?

What impact does a negative y-intercept have on the graph of a linear function?

How does increasing the absolute value of 'a' in the equation y = ax^2 + q affect the graph of the parabola?

Which of the following accurately describes the range of a quadratic function when 'a' is less than zero?

What is the effect of 'q' when it is a positive value in the function y = ax^2 + q?

What principle defines the steepness of the graph in relation to the gradient 'm' for a linear function?

What is the significance of checking for extraneous solutions after solving an equation?

In the context of solving quadratic equations, what format must be achieved for the equation before applying factorization?

What must be ensured when applying operations to both sides of an equation?

When solving simultaneous equations using substitution, what is typically the first step?

How many solutions can a quadratic equation have under certain conditions?

What is the purpose of factoring out common terms when solving linear equations?

What common mistake should be avoided when rearranging terms in an equation?

Which characteristic differentiates linear equations from quadratic equations?

What is typically the last step after finding solutions for simultaneous equations?

What unique feature applies to quadratic equations when considering their solutions?

What happens to the graph of the function when the parameter q is set to a negative value?

If a function is defined as y = 3(2^x) - 5, what is the y-intercept of the graph?

How is the amplitude of the sine function affected when a > 1?

For a cosine function of the form y = -2 ext{cos}( heta) + 3, what is the range of the function?

In the equation of the tangent function y = 5 ext{tan}( heta) + 2, what effect does the factor of 5 have on the graph?

What is the period of the function y = 4 ext{sin}(2 heta) + 1?

How does the value of b in the exponential function y = ab^x influence the graph if 0 < b < 1?

In the context of the sine function, which of the following statements is true when a < 0?

What vertical shift occurs in the function y = ext{sin}( heta) + 4?

In an exponential function of the form y = ab^x + q, which conditions on a and b will result in a graph curving downwards?

What does the parameter 'q' do in the equations for parabolas and hyperbolas?

Which of the following statements accurately describes the asymptotes of a hyperbola?

In determining the equation of a sine function, what indicates the amplitude?

How is the range defined for trigonometric functions like sine and cosine?

What is the correct process to find the value of 'a' in the equation of a hyperbola?

What does the sign of 'a' in the equation of a parabola indicate?

How would you describe the domains of trigonometric functions like tangent?

When determining the characteristics of the graph of a tangent function, which feature is crucial?

What characteristic is critical in differentiating between the functions y = ax^2 + q and y = a/x + q?

What impact does increasing the absolute value of 'a' have on the graph of a tangent function?

Which number set includes all numbers that can be expressed as a ratio of two integers?

Which of the following options describes all possible values in the real number system?

What distinguishes irrational numbers from rational numbers?

Which set of numbers does NOT include negative values?

Which of the following symbols represents the set of integers?

Which statement best describes imaginary numbers?

Which of the following best describes a rational number?

What differentiates an irrational number from a rational number?

In converting a recurring decimal into a rational number, what is the primary operation performed?

How does rounding off a number change its value?

Which of the following statements accurately describes perfect squares in the context of surds?

When estimating a surd, what should you primarily identify?

In rounding off a decimal number, what does a digit of 9 result in during the rounding process?

Which of the following types of decimal numbers are classified as rational numbers?

What component of a mathematical expression is defined as a numerical factor?

What is the interpretation of the value of 'm' in the equation y = mx + c?

If the y-intercept 'c' is negative in the equation y = mx + c, how does this affect the graph?

What does an upward opening parabola indicate about the value of 'a' in the equation y = ax^2 + q?

In the function y = ax^2 + q, how does adjusting 'q' impact the graph?

What characterizes the turning point of a parabola when 'a' is negative?

Which statement about the domain of the function y = ax^2 + q is correct?

How does a value of 'a' between 0 and 1 affect the graph of y = ax^2 + q?

What happens to the graph of y = mx + c if 'm' is zero?

What is the effect of a positive value of 'q' in the function y = ax^2 + q?

What is the result of simplifying the expression $\frac{a^5}{a^2} \times a^3$?

If $a^x = a^y$, what can be concluded when $a > 0$ and $a \neq 1$?

Which property applies to the expression $(ab)^{m/n}$?

What happens when simplifying the expression $rac{a^{m/n}}{a^{p/q}}$?

Which expression corresponds to the zero exponent rule?

What is the first step to solve the equation $a^{x} = b^{y}$ using logarithms?

How can the expression $rac{a^{1/n}}{b^{1/n}}$ be rewritten?

When factorizing an expression of the form $x^2 - 9$, what is the correct factorization?

Which of the following describes how to simplify the expression $(a^2b^3)^{3/2}$?

What is the maximum number of solutions a linear equation can have?

What is the result of multiplying the monomial 5 and the binomial (3x + 2)?

Which step is essential after factoring a quadratic equation to ensure the solution is valid?

In the elimination method for solving simultaneous equations, what operation is commonly used to eliminate a variable?

Which of the following correctly expands the binomials (x + 3) and (2x - 5)?

What is the first step in factoring the quadratic trinomial 3x^2 + 12x + 12?

What type of equation allows only one solution as opposed to potentially two solutions?

When simplifying the fraction ( \frac{x^2 - 1}{x^2 + x - 2} ), what expression is factored in the denominator?

When solving a quadratic equation using factoring, which form should the equation be in before applying the method?

What is a necessary condition for any operation performed on one side of an equation?

What identity can be used to factor the expression x^3 - 8?

Which method involves pairing and factoring terms in the expression x^3 + 3x^2 + 2x?

Which method is efficient for simplifying the number of equations in simultaneous equations?

In solving simultaneous equations, how many equations are required to find the values of two unknowns?

In the expression ( \frac{3x^2 + 6x}{3x} ), after canceling common factors, what remains?

What is often the first step when expanding expressions while solving linear equations?

Factoring the expression 4x^2 - 16 involves recognizing which type of factorization?

When a quadratic equation has no real solutions, what can typically be inferred about its discriminant?

What is the result of simplifying the expression ( \frac{x^3 - 1}{x - 1} )?

What is the correct method used to multiply a binomial by a trinomial?

What does the solution of a system of simultaneous equations represent when solved graphically?

Which step is crucial when translating words into algebraic expressions for word problems?

When solving literal equations, which principle is important to isolate the unknown variable?

What happens to the inequality symbol when both sides of a linear inequality are divided by a negative number?

In the equation of a line, what does the value of c represent?

What must be done if the unknown variable in a literal equation is part of multiple terms?

What approach should be taken when solving a word problem that involves multiple steps?

Which of the following statements holds true regarding the value of m in a linear function?

When solving a linear inequality such as $2x + 2 < 1$, what is the first step?

What is necessary to check once a set of equations from a word problem is solved?

What effect does the parameter $q$ have in the equations of the hyperbola and tangent functions?

How does the sign of $a$ influence the shape of a parabola?

What can be inferred about the range of the function $y = a an heta + q$?

Which characteristics can be determined from the asymptotes of the tangent function?

When solving for $a$ in the equation of a hyperbola $y = rac{a}{x} + q$, what method must be used?

What is the primary goal when determining the equation of a parabola using its sketch?

In which scenario is it necessary to set $y = 0$ to find the x-intercept for parabolic graphs?

Which equation represents the graph of a sine function modified by vertical shifts and amplitude?

What defines the domain of the tangent function based on its behavior?

What determines the direction in which an exponential graph curves when both $a$ and $b$ are greater than 1?

Which of the following accurately describes the behavior of the sine function at its minimum turning point?

What effect does a negative value of $a$ have on the graph of a sine function?

For a cosine function $y = a , cos , heta + q$, which condition indicates a vertical compression?

What happens to the horizontal asymptote of an exponential function when $q < 0$?

Which of the following describes the domain of the tangent function?

How does the value of $b$ influence an exponential function of the form $y = ab^x + q$?

What is the period of the sine function expressed as $y = ext{sin} heta$?

Which point represents the y-intercept of the function $y = an heta$?

What is the range of a function of the form $f(x) = ax^2 + q$ when $a < 0$?

At what point does the turning point occur for the graph of $f(x) = ax^2 + q$?

What is the effect of setting $x = 0$ on the hyperbolic function $y = rac{a}{x} + q$?

Which of the following statements accurately describes the horizontal asymptote of the function $y = rac{a}{x} + q$?

What is the domain of the hyperbolic function $y = rac{a}{x} + q$?

In the equation of an exponential function $y = ab^x + q$, what does a positive value of $a$ indicate?

For the function $y = ax^2 + q$, if $a$ is negative, which of the following is true?

What describes the axes of symmetry for the function $y = rac{a}{x} + q$?

When designing a graph for $f(x) = ax^2 + q$, which characteristic must be established first?