Chapter 2: Quadratic Functions

y intercept

y intercept

The ________ is c; the point (0, c) is on the parabola.

Axis of Symmetry

________- a line that divides a parabola into mirror images and passes through the vertex; the ________ is the vertical line x= h or x=- b /2a.

quadratic function

For the ________ f (x)= ax2 + bx + c, the y- coordinate of the vertex is the minimum value of the function when a> 0 and the maximum value when a <0.

Lesson 1

Transformations of Quadratic Functions

A quadratic function is a function that can be written in the form f(x) = a(x

h)2 + k, where a ≠ 0

The vertex form of a quadratic function is f(x) = a(x

h)2 + k, where a ≠ 0 and the vertex is (h, k)

Lesson 2

Characteristics of Quadratic Functions

Axis of Symmetry

a line that divides a parabola into mirror images and passes through the vertex; the axis of symmetry is the vertical line x = h or x = -b/2a

Standard Form

a quadratic function written in the form f(x) = ax2 + bx + c

Minimum value

f(-b/2a)

Domain

all real numbers

Range

y ≥ f(-b/2a)

Maximum value

f(-b/2a)

Domain

all real numbers

Range

y ≤ f(-b/2a)

Lesson 3

Modeling with Quadratic Equations

quadratic function

a function that can be written in the form f(x) = a(x - h)2 + k, where a ≠ 0

parabola

the U-shaped graph of a quadratic function

vertex

the lowest part on a parabola that opens up or the highest point on a parabola that opens down

vertex form

f(x) = a(x - h)2 + k, where a ≠ 0 and the vertex is (h, k)

axis of symmetry

a line that divides a parabola into mirror images and passes through the vertex; the axis of symmetry is the vertical line x = h or x = -b/2a

standard form

a quadratic function written in the form f(x) = ax2 + bx + c

intercept form

a quadratic function in the form f(x) = a(x - p)(x - q)

minimum value

the y-coordinate of the vertex when a > 0

maximum value

the y-coordinate of the vertex when a < 0