Algebra 1: Chapter 8 Flashcards

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.