14 Questions
Which type of function can be represented as a straight line?
Continuous function
What is the end behavior of a graph of a quadratic equation with a positive leading coefficient?
Rising on both ends
What is the slope of a line parallel to the line with equation $3x - 4y = 8$?
$3/4$
In a system of equations, what does it mean if there are no solutions?
The system is inconsistent
Which type of function can be represented by a graph that does not have any breaks or holes?
Non-linear function
What is the y-intercept of the line with equation $2x - 3y = 6$?
$(0, 3)$
In a system of 3 equations and 3 unknowns, how many solutions are possible?
One solution
What is the discriminant of a quadratic equation used to determine?
The number of solutions and their nature
What type of equation can be represented by a graph that forms a U-shaped curve?
Quadratic equation
Match the following functions with their characteristics:
Continuous function = Can be graphed without lifting the pencil Linear function = Graph is a straight line Piecewise function = Defined by different equations for different intervals Quadratic function = Graph is a parabola
Match the following equations with their graph characteristics:
Graph a line = Represents a straight line Graph a quadratic inequality = Represents a U-shaped curve with shading for inequality Graph a linear inequality = Represents a shaded region on either side of a line Graph a parabola = Represents a U-shaped curve
Match the following equations with their solutions methods:
Solve an equation = Find the value(s) of the variable that make the equation true Solve an inequality = Find the range of values for which the inequality is true Solve an absolute value equation = Find the values that satisfy the equation and its absolute value Simplify complex numbers with all operations = Perform arithmetic operations on complex numbers
Match the following systems with their characteristics:
Solve a system of equations = Find the common solution(s) to two or more equations Solve a system of 3 equations and 3 unknowns = Find the values of three unknowns that satisfy three equations simultaneously Know the types of systems of equations = Understand different classifications based on their solutions Given a graph, determine the linear inequalities = Interpret and write inequalities based on graph regions
Match the following quadratic equation forms with their descriptions:
Write a quadratic equation in vertex form = Represent a parabola using its vertex and transformations Find the discriminant and determine the type and number of solutions = Identify nature of solutions based on discriminant value Projectile problem = Real-life application involving parabolic motion Solve quadratic equations by factoring = Use factorization to find roots/solutions of quadratic equations
Study Notes
Linear Functions
- A linear function can be represented as a straight line.
Quadratic Equations
- The end behavior of a graph of a quadratic equation with a positive leading coefficient is that the graph opens upward.
- A quadratic equation can be represented by a graph that forms a U-shaped curve.
Slope
- The slope of a line parallel to the line with equation $3x - 4y = 8$ is $\frac{3}{4}$.
Systems of Equations
- If there are no solutions in a system of equations, it means that the lines are parallel and do not intersect.
- In a system of 3 equations and 3 unknowns, there are three possible solutions: one unique solution, no solution, or infinitely many solutions.
Graph Characteristics
- A graph that does not have any breaks or holes represents a continuous function.
Y-Intercept
- The y-intercept of the line with equation $2x - 3y = 6$ is 2.
Discriminant
- The discriminant of a quadratic equation is used to determine the number of solutions.
Function Characteristics
- Match the following functions with their characteristics:
- Linear functions: can be represented as a straight line
- Quadratic functions: can be represented by a graph that forms a U-shaped curve
- Continuous functions: can be represented by a graph that does not have any breaks or holes
Equation Characteristics
- Match the following equations with their graph characteristics:
- Linear equations: straight line
- Quadratic equations: U-shaped curve
Solution Methods
- Match the following equations with their solutions methods:
- Linear equations: substitution, elimination, or graphing
- Quadratic equations: factoring, quadratic formula, or graphing
System Characteristics
- Match the following systems with their characteristics:
- System of 2 equations and 2 unknowns: one unique solution, no solution, or infinitely many solutions
- System of 3 equations and 3 unknowns: one unique solution, no solution, or infinitely many solutions
Quadratic Equation Forms
- Match the following quadratic equation forms with their descriptions:
- Standard form: $ax^2 + bx + c = 0$
- Vertex form: $a(x - h)^2 + k = 0$
- Factored form: $a(x - r)(x - s) = 0$
Test your knowledge of algebra functions, graphing techniques, solving equations and inequalities, and understanding systems of equations in this quiz.
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