Algebra 1: Chapter 8 Flashcards

Questions and Answers

What is the average rate of change?

f(b) - f(a) / b - a

What is the axis of symmetry?

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

What is an even function?

f(-x) = f(x)

What is intercept form?

f(x) = a(x - p)(x - q) where a ≠ 0 Signup and view all the answers

What is the maximum value of a quadratic function?

The y-coordinate of the vertex of the quadratic function f(x) = ax^2 + bx + c, where a > 0 Signup and view all the answers

What is the minimum value of a quadratic function?

The y-coordinate of the vertex if a > 0 for y = ax^2 + bx + c Signup and view all the answers

What is an odd function?

f(-x) = -f(x) Signup and view all the answers

What is a parabola?

The U-shaped graph of a quadratic function 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 a parabola?

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

What is a zero of a function?

An x-value that makes the function equal to 0 Signup and view all the answers

Study Notes

Average Rate of Change

Calculated using the formula: ( \frac{f(b)-f(a)}{b-a} )
Represents how a function changes on average over an interval.

Axis of Symmetry

A line that bisects a figure or graph into two identical halves.
Critical in analyzing the shape of parabola graphs.

Even Function

Defined by the property: ( f(-x) = f(x) )
Symmetrical about the y-axis, meaning both sides of the graph mirror each other.

Intercept Form

A quadratic function expressed as ( f(x) = a(x - p)(x - q) ) where ( a \neq 0 )
Represents the function's x-intercepts at points ( p ) and ( q ).

Maximum Value

The highest y-coordinate of a quadratic function's vertex when ( a > 0 ).
Important for determining the peak value of upward-opening parabolas.

Minimum Value

The lowest y-coordinate of a quadratic function's vertex when ( a > 0 ).
Critical for defining the lowest point on upward-opening parabolas.

Odd Function

Characterized by the relation: ( f(-x) = -f(x) )
Exhibits rotational symmetry about the origin.

Parabola

U-shaped graph representing quadratic functions.
Can open upward or downward, depending on the coefficient ( a ).

Vertex Form of a Quadratic Function

Written as ( y = a(x - h)^2 + k )
Provides crucial information about the vertex's position and the graph's direction.

Vertex of a Parabola

The point at which the parabola reaches its maximum or minimum value.
Essential in graphing and understanding the behavior of quadratic functions.

Zero of a Function

An x-value that causes the function to equal zero.
Indicates the points where the graph intersects the x-axis, also known as roots or x-intercepts.

Description

Test your knowledge on key concepts from Algebra 1, Chapter 8 with these flashcards. You'll encounter terms like average rate of change, axis of symmetry, and even function. Perfect for reviewing and reinforcing your understanding of quadratic functions and their properties.