Algebra 2 Chapter 5 Flashcards

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Questions and Answers

What is a quadratic function?

f(x) = a(x - h)^3 + k

f(x) = ax^2 + bx + c

f(x) = a(x - h)^2 + k (a ≠ 0) (correct)

f(x) = a(x + h)^2 + k

Define a parabola.

U-shaped curve

What is the axis of symmetry in relation to a parabola?

The line through the vertex that divides the parabola into two congruent halves.

What is the standard form of a quadratic function?

f(x) = ax^2 + bx + c Signup and view all the answers

What is the minimum value of a parabola when it opens upward?

The y-value of the vertex. Signup and view all the answers

What is the maximum value of a parabola when it opens downward?

The y-value of the vertex. Signup and view all the answers

What is a zero of a function?

A value of x that makes f(x) equal zero. Signup and view all the answers

What are the roots of an equation?

Values of the variable that make the equation true. Signup and view all the answers

Define binomials.

Quadratic expressions with two terms. Signup and view all the answers

Define trinomials.

Quadratic expressions with three terms. Signup and view all the answers

What does completing the square involve?

Adding a term to form a perfect square trinomial. Signup and view all the answers

What is the imaginary unit?

i, defined as -1 square rooted. Signup and view all the answers

Define the vertex of a parabola.

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

What is the vertex form of a quadratic function?

f(x) = a(x - h)^2 + k Signup and view all the answers

What is an imaginary number?

The square root of a negative number. Signup and view all the answers

Define a complex number.

A number that can be written in the form a + bi. Signup and view all the answers

What is the real part of a complex number?

Complex numbers where b = 0. Signup and view all the answers

What is the imaginary part of a complex number?

Complex numbers where a = 0 and b is not equal to 0. Signup and view all the answers

Define a complex conjugate.

The complex number a - bi. Signup and view all the answers

What is a quadratic inequality in two variables?

An inequality where a, b, and c are real numbers and a does not equal 0. Signup and view all the answers

What is the absolute value of a complex number?

The distance from the origin to the point (a, b) in the complex plane. Signup and view all the answers

Define the complex plane.

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

What is the discriminant in relation to the quadratic formula?

It helps determine the number of real roots of a quadratic equation. Signup and view all the answers

What is quadratic regression?

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

What is a quadratic model?

A quadratic function that represents a real data set. Signup and view all the answers

Study Notes

Quadratic Functions and Properties

A quadratic function is represented as f(x) = a(x - h)² + k, where a ≠ 0.
The parabola is the graph of a quadratic function, characterized by its U-shape.

Key Features of Parabolas

The axis of symmetry is a vertical line that runs through the vertex, dividing the parabola into two equal parts.
The vertex is the highest or lowest point of the parabola, indicating the maximum or minimum value depending on its orientation.

Standard Forms and Types

Standard form of a quadratic function is given by f(x) = ax² + bx + c.
Binomials are quadratic expressions featuring two terms.
Trinomials consist of three terms, representing more complex quadratic expressions.

Solutions and Values

A zero of a function occurs at point x where f(x) = 0, indicating the x-intercepts of the graph.
The roots of an equation are values that satisfy the equation.

Transformation Techniques

Completing the square involves adding a term to create a perfect square trinomial, facilitating easier graphing and analysis.

Imaginary and Complex Numbers

The imaginary unit i equals √(-1), a fundamental concept in complex numbers.
Imaginary numbers are defined as the square roots of negative numbers.
A complex number is expressed in the form a + bi, where a is the real part and b is the imaginary part.

The Complex Plane

Real part refers to complex numbers where b = 0, while the imaginary part consists of numbers where a = 0 and b ≠ 0.
The complex conjugate of a + bi is a - bi, an important relationship in complex number operations.
The complex plane represents real numbers on the horizontal axis and imaginary numbers on the vertical axis.

Quadratic Inequalities and Applications

A quadratic inequality in two variables features real numbers a, b, and c, with a ≠ 0.
The discriminant within the Quadratic Formula helps ascertain the number of real roots for a quadratic equation.
Quadratic regression is a technique for generating a quadratic model based on a data set, useful in statistical analysis.
A quadratic model is essentially a quadratic function that accurately reflects a given data set.

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Description

Test your understanding of key concepts in Algebra 2 Chapter 5 with these flashcards. Covering essential terms such as quadratic functions, parabolas, and the axis of symmetry, this quiz will help reinforce your knowledge. Perfect for reviewing before exams or enhancing your understanding of algebra.