Applied Algebra B - Quadratic Functions Review

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Questions and Answers

What is the axis of symmetry?

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

What is the equation for finding the axis of symmetry?

x = -b/2a

What is the maximum value?

The largest value in a set of data.

What is the minimum value?

The smallest value in a set of data. Signup and view all the answers

What shape does a parabola represent?

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

What is a quadratic function?

A function in which the greatest power of the variable is 2. Signup and view all the answers

What is the vertex form of a quadratic function?

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

What is the vertex of the parabola?

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

What is the standard form of a quadratic function?

Ax + By = C Signup and view all the answers

What is the difference of two squares?

A polynomial that can be factored as the product of the sum and difference of two terms. Signup and view all the answers

What does factoring mean?

To express a polynomial as the product of monomials and polynomials. Signup and view all the answers

What is the greatest common factor?

The largest factor that two or more numbers have in common. Signup and view all the answers

What is a perfect square trinomial?

A trinomial that is the square of a binomial. Signup and view all the answers

What is a zero of a function?

For the function f, any number x such that f(x) = 0. Signup and view all the answers

What is the Zero-Product Property?

When the product of two or more factors is zero, one of the factors must equal zero. Signup and view all the answers

What is a discriminant?

A function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial. Signup and view all the answers

What is the quadratic formula?

x = -b ± √(b² - 4ac)/2a Signup and view all the answers

What is completing the square?

A process used to make a quadratic expression into a perfect square trinomial. Signup and view all the answers

How do you find the number of solutions of a quadratic equation?

By evaluating the discriminant. Signup and view all the answers

What is a domain in relation to a quadratic function?

x values Signup and view all the answers

What is the range of a quadratic function?

All possible y values. Signup and view all the answers

Study Notes

Quadratic Functions and Equations Key Terms

Axis of Symmetry: A line that divides a parabola into two mirrored halves, essential for graphing quadratic functions.
Axis of Symmetry Equation: Calculated using the formula x = -b/2a; determines the vertical line that runs through the vertex.
Maximum Value: The peak point of a quadratic function; represents the largest output of the function.
Minimum Value: The lowest point of a quadratic function; indicates the smallest output of the function.
Parabola: The graphical representation of a quadratic function, characterized by its U-shaped curve.
Quadratic Function: A polynomial function where the highest exponent is 2, generally expressed as y = ax² + bx + c.
Vertex Form: A way of expressing a quadratic function, given by the equation y = a(x - h)² + k, where (h, k) is the vertex.
Vertex of the Parabola: The turning point of the parabola, indicating either the maximum or minimum value depending on the orientation of the parabola.
Standard Form: A typical expression format for linear equations, represented as Ax + By = C.
Difference of Two Squares: A special product result allowing the factoring of expressions in the form a² - b² as (a + b)(a - b).
Factoring: The process of breaking down a polynomial into simpler components that, when multiplied together, yield the original polynomial.
Greatest Common Factor (GCF): The largest shared factor of two or more numbers, useful in simplifying expressions.
Perfect Square Trinomial: A trinomial that results from the square of a binomial, formatted as (a ± b)².
Zero of a Function: A value of x for which the function f(x) equals zero; the x-intercepts of the graph of the function.
Zero-Product Property: If the product of multiple factors equals zero, at least one factor must also be zero; a fundamental concept in solving polynomial equations.
Discriminant: A calculated part of the quadratic formula (b² - 4ac) that indicates the nature and number of roots of the equation.
Quadratic Formula: An essential formula for finding the roots of a quadratic equation: x = (-b ± √(b² - 4ac)) / (2a).
Completing the Square: A method for transforming a quadratic expression into a perfect square trinomial to simplify solving.

Understanding Solutions and Function Characteristics

Finding the Number of Solutions: Analyze the discriminant; if it's positive, there are two distinct solutions, if zero, one solution, and if negative, no real solutions.
Domain: Refers to all possible x-values for the quadratic function, typically all real numbers.
Range: All potential y-values of a quadratic function, determined by the direction of the parabola (upward or downward based on the coefficient a).

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Description

Prepare for your Applied Algebra B unit test with this comprehensive review of key terms and concepts related to quadratic functions and equations. This set of flashcards covers definitions, equations, and examples to reinforce your understanding. Get ready to ace your test!