Algebra 2 Terms Flashcards

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Questions and Answers

What is the absolute value of a complex number?

Distance from the origin to the point in the complex plane (correct)

The square root of the sum of squares of its real and imaginary parts (correct)

The product of its real and imaginary parts

None of the above

What is the axis of symmetry?

A line that divides a plane figure or a graph into two congruent reflected halves.

What is a binomial?

A polynomial with two terms.

What does completing the square involve?

Forming a perfect square of x² + bx. Signup and view all the answers

What is a complex conjugate?

The complex conjugate of a complex number a+bi is a-bi. Signup and view all the answers

What is a complex number?

Any number that can be written as a+bi. Signup and view all the answers

What does the complex plane consist of?

A set of coordinate axes where the horizontal axis is the real axis and the vertical axis is the imaginary axis. Signup and view all the answers

What is the discriminant in a quadratic equation?

b² - 4ac. Signup and view all the answers

What is an imaginary number?

The square root of a negative number, written in the form bi. Signup and view all the answers

What is the imaginary part of a complex number?

The real number b in the form a+bi, represented graphically on the imaginary axis. Signup and view all the answers

What is the maximum value in the context of graphing a function?

The y-value of the highest point on the graph of the function. Signup and view all the answers

What is the minimum value in the context of graphing a function?

The y-value of the lowest point on the graph of the function. Signup and view all the answers

What is a parabola?

The shape of the graph of a quadratic function. Signup and view all the answers

What is a quadratic function?

A function of the form ax² + bx + c. Signup and view all the answers

What is a quadratic inequality?

An inequality in the form y < ax² + bx + c or y > ax² + bx + c. Signup and view all the answers

What is a quadratic model?

A quadratic function used to represent a set of data. Signup and view all the answers

What is quadratic regression?

A statistical method used to fit a quadratic model to a given data set. Signup and view all the answers

What is the real part of a complex number?

The real number a in the form a+bi. Signup and view all the answers

What is the root of an equation?

Any value of the variable that makes the equation true. Signup and view all the answers

What is standard form in a polynomial?

The form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Signup and view all the answers

What is a trinomial?

A polynomial with three terms. Signup and view all the answers

What is the vertex form of a quadratic function?

f(x) = a(x-h)² + k, where (h,k) is the vertex. Signup and view all the answers

What is the vertex of the parabola?

The highest or lowest point on the parabola. Signup and view all the answers

What is zero of a function?

Any number x such that f(x) = 0. Signup and view all the answers

What is the degree of a monomial?

The sum of exponents of the variables in the monomial. Signup and view all the answers

What is the degree of a polynomial?

The degree of the term of the polynomial with the greatest degree. Signup and view all the answers

What is end behavior?

The trends in y-values of a function as the x-values approach positive and negative infinity. Signup and view all the answers

What is the leading coefficient?

The coefficient of the first term of a polynomial in standard form. Signup and view all the answers

What is a local maximum?

The highest point in a localized region of a graph. Signup and view all the answers

What is a local minimum?

The lowest point in a localized region of a graph. Signup and view all the answers

What is a monomial?

A number or product of numbers and variables with whole-number exponents, or a polynomial with one term. Signup and view all the answers

What is a polynomial?

A monomial or a sum or difference of monomials. Signup and view all the answers

What is a polynomial function?

A function whose rule is a polynomial. Signup and view all the answers

What is synthetic division?

A shorthand method of dividing by a linear binomial. Signup and view all the answers

What is a turning point?

A point on the graph of a function where it changes from increasing to decreasing or vice versa. Signup and view all the answers

What is an asymptote?

A line that a graph approaches as the value of a variable becomes extremely large or small. Signup and view all the answers

What is a common logarithm?

A logarithm whose base is 10. Signup and view all the answers

What is exponential decay?

The form f(x) = ab where b < 1. Signup and view all the answers

What is an exponential equation?

An equation in which the variable appears in the exponent. Signup and view all the answers

What is an exponential function?

A function in the form f(x) = ab with an exponent of x. Signup and view all the answers

What is exponential growth?

The form f(x) = ab where b > 1. Signup and view all the answers

What is exponential regression?

A statistical method used to fit an exponential model to data. Signup and view all the answers

What is an inverse function?

The function that results from exchanging the input and output values of a one-to-one function. Signup and view all the answers

What is an inverse relation?

The set of all ordered pairs (y,x) derived from a relation of ordered pairs (x,y). Signup and view all the answers

What is a logarithm?

The exponent that a specified base must be raised to in order to get a certain value. Signup and view all the answers

What is a logarithmic equation?

An equation that contains a logarithm of a variable. Signup and view all the answers

What is logarithmic regression?

A statistical method used to fit a logarithmic model to a given data set. Signup and view all the answers

What is a natural logarithm?

A logarithm with base e, written as ln. Signup and view all the answers

What is a natural logarithmic function?

The function f(x) = ln x, which is the inverse of the natural exponential function. Signup and view all the answers

What is combined variation?

A relationship containing both direct and inverse variation. Signup and view all the answers

What is a complex fraction?

A fraction that contains one or more fractions in the numerator, the denominator, or both. Signup and view all the answers

What is the constant of variation?

The constant k in direct, inverse, joint, and combined variation equations. Signup and view all the answers

What is a continuous function?

A function whose graph is an unbroken line or curve with no gaps or breaks. Signup and view all the answers

What is direct variation?

A linear relationship between two variables that can be expressed as y = kx. Signup and view all the answers

What is a discontinuous function?

A function whose graph has one or more jumps, breaks, or holes. Signup and view all the answers

What is an extraneous solution?

A solution of a derived equation that is not a solution of the original equation. Signup and view all the answers

What is a hole in a graph?

An omitted point on a graph. Signup and view all the answers

What is inverse variation?

A relationship between two variables that can be expressed as y = k/x. Signup and view all the answers

What is joint variation?

A relationship among three variables that can be expressed as y = kxz. Signup and view all the answers

What is a radical equation?

An equation that contains a variable within a radical. Signup and view all the answers

What is a radical function?

A function whose rule contains a variable within a radical. Signup and view all the answers

What is a radical inequality?

An inequality that contains a variable within a radical. Signup and view all the answers

What is a rational equation?

An equation that contains one or more rational expressions. Signup and view all the answers

What is a rational exponent?

An exponent that is a fraction. Signup and view all the answers

What is a rational expression?

An algebraic expression whose numerator and denominator are polynomials. Signup and view all the answers

What is a rational function?

A function whose rule can be written as a rational expression. Signup and view all the answers

What is a rational inequality?

An inequality that contains one or more rational expressions. Signup and view all the answers

What is a square-root function?

A function whose rule contains a variable under a square-root sign. Signup and view all the answers

Study Notes

Algebra 2 Terms

Absolute Value of a Complex Number: Denoted |a+bi|, it represents the distance from the origin to the point (a,b) in the complex plane, calculated as √(a² + b²).
Axis of Symmetry: A line that evenly divides a plane figure or a graph into two congruent, mirrored halves.
Binomial: A type of polynomial that consists of exactly two terms.
Completing the Square: A technique for transforming a quadratic expression into a perfect square of the form x² + bx.
Complex Conjugate: For a complex number a+bi, its conjugate is represented as a-bi.
Complex Number: A number that can be expressed in the form a+bi.
Complex Plane: A coordinate system where the horizontal axis is real and the vertical axis is imaginary.
Discriminant: In the quadratic formula, represented as b² - 4ac, it determines the nature of the roots.
Imaginary Number: Defined as the square root of a negative number, expressed in the form bi, where b is a real number and i is the imaginary unit.
Imaginary Part: Referring to the term b in a complex number a+bi, represented graphically on the imaginary axis.
Imaginary Unit: Represented as i, it is used as the base in imaginary numbers.
Maximum Value: The highest y-value point on the graph of a function.
Minimum Value: The lowest y-value point on the graph of a function.
Parabola: The characteristic shape of a graph representing a quadratic function.
Quadratic Function: Expressed as ax² + bx + c, it describes a polynomial of degree 2.
Quadratic Inequality: Inequalities that can be expressed in various forms involving a quadratic equation.
Quadratic Model: A statistical representation using a quadratic function to fit a dataset.
Quadratic Regression: A method used to find a quadratic model that best fits a given set of data.
Real Part: The coefficient a in a complex number a+bi, representing the real component.
Root of an Equation: Values of the variable that satisfy the equation, making it true.
Standard Form: The equation format ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.
Trinomial: A polynomial with three distinct terms.
Vertex Form: A way to express a quadratic function as f(x) = a(x-h)² + k, where (h,k) is the vertex.
Vertex of the Parabola: The peak or trough point of the parabola indicating maximum or minimum values.
Zero of a Function: Any value x such that f(x) = 0.
Degree of a Monomial: Calculated as the sum of the exponents of the variables within the monomial.
Degree of a Polynomial: The highest degree among the polynomial's terms.
End Behavior: Refers to how the y-values of a function behave as the x-values approach infinity or negative infinity.
Leading Coefficient: The coefficient of the term with the highest degree in a polynomial written in standard form.
Local Maximum: A point where the function reaches a peak within a specified interval.
Local Minimum: A point where the function reaches a trough within a specified interval.
Monomial: An expression composed of a single term featuring numbers and variables raised to whole number powers.
Polynomial: Comprises monomials combined through addition or subtraction.
Polynomial Function: A function defined where its output follows a polynomial expression.
Synthetic Division: A simplified method for dividing polynomials by linear binomials, only using coefficients.
Turning Point: A point where the function changes from increasing to decreasing, or vice versa.
Asymptote: A line that a graph approaches as the variable grows infinitely large or small.
Common Logarithm: A logarithm with base 10.
Exponential Decay: Described by f(x) = ab^x, where b < 1, indicating a decrease over time.
Exponential Function: Defined as f(x) = ab^x, showcasing growth or decay based on the value of b.
Exponential Growth: Expressed as f(x) = ab^x, where b > 1, indicating growth over time.
Exponential Regression: A technique for fitting an exponential model to data.
Inverse Function: A function created by swapping input and output values of a one-to-one function.
Inverse Relation: The relation formed when pairs (x,y) are converted to (y,x), resulting in reflection across y=x.
Logarithm: An exponent indicating how many times a base is multiplied to achieve a particular value.
Logarithmic Equation: An equation that involves logarithms of variables.
Natural Logarithm: A logarithm with base e, usually written as ln.
Combined Variation: A relationship that includes both direct and inverse variation.
Complex Fraction: Any fraction containing one or more fractions in its numerator, denominator, or both.
Constant of Variation: The constant k in equations relating to direct, inverse, joint, or combined variation.
Continuous Function: A function depicted by an unbroken line or curve without gaps.
Direct Variation: A relationship between two variables, expressed as y = kx, where k is non-zero.
Discontinuous Function: A function whose graph exhibits jumps, breaks, or holes.
Extraneous Solution: A derived solution that does not satisfy the original equation.
Hole in a Graph: A point that is omitted from the graph.
Inverse Variation: Describes a relationship y = k/x, indicating an inverse connection between variables.
Joint Variation: A relationship among three variables expressed in the form y = kxz.
Radical Equation: An equation containing a variable within a radical expression.
Radical Function: A function that incorporates a variable inside a radical expression.
Radical Inequality: An inequality that features a variable within a radical.
Rational Equation: An equation that includes one or more rational expressions.
Rational Expression: An algebraic fraction where both the numerator and denominator are polynomials, with the denominator's degree ≤ 1.
Rational Function: A function written as a rational expression.
Rational Inequality: An inequality that contains one or more rational expressions.
Square-Root Function: A function defined by a rule containing a variable under a square-root.

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Test your knowledge with these flashcards on key Algebra 2 terms. Each card features important definitions and concepts that are essential to mastering the subject. Perfect for quick reviews and strengthening your understanding of algebraic principles.