9.4 Graphing Quadratics

Three Forms

A quadratic equation can be written in three different forms: form,

form, and form.

In order to graph each form, we need four key points and a key axis. The method to find these varies by form.

vertex axis of symmetry x-intercepts y-intercept

vertexstandardfactored

The vertex form of a quadratic equation is:

The graph the function is a parabola with vertex at . The parabola is symmetric with respect to the line

. If , the parabola opens ; if

, the parabola opens .

Vertex Form

f x a x h 2 k

h,k

x h a 0a 0upward

downward

1.

a. Find the vertex.

b. Find the axis of symmetry.

c. Find the x-intercepts (let y=0)

d. Find the y-intercept (let x=0)

Graph the parabola.

f x 2 x 3 2 8

2.

a. Find the vertex.

b. Find the axis of symmetry.

c. Find the x-intercepts (let y=0)

d. Find the y-intercept (let x=0)

Graph the parabola.

f x x 3 2 1

The vertex form of a quadratic equation is:

The graph the function is a parabola with

vertex at . The parabola is symmetric with respect to the line

. If , the parabola opens ; if , the parabola opens .

Standard Form

b

2a, f

b

2a

x b

2a a 0a 0upward

downward

f x ax2 bx c

3.

a. Find the vertex.

b. Find the axis of symmetry.

c. Find the x-intercepts (let y=0)

d. Find the y-intercept (let x=0)

Graph the parabola.

f x x2 2x 1

4.

a. Find the vertex.

b. Find the axis of symmetry.

c. Find the x-intercepts (let y=0)

d. Find the y-intercept (let x=0)

Graph the parabola.f x 2x2 7x 4

The vertex form of a quadratic equation is:

The graph the function is a parabola with

vertex at . The parabola is symmetric with respect to the line

. If , the parabola opens ; if , the parabola opens .

Factored Form

r1 r22, f

r1 r22

x r1 r22 a 0

a 0upwarddownward

f x a x r1 x r2

5.

a. Find the vertex.

b. Find the axis of symmetry.

c. Find the x-intercepts (let y=0)

d. Find the y-intercept (let x=0)

Graph the parabola.

f x 12x 1 x 5

6.

a. Find the vertex.

b. Find the axis of symmetry.

c. Find the x-intercepts (let y=0)

d. Find the y-intercept (let x=0)

Graph the parabola.

f x x 3 x 2

7. The parabola has a vertex at and passes through the point

Write the equation in vertex form.

2, 5 3,0

8. The parabola has a = 2, had x = -3 as its axis of symmetry, and passes through the point

Write the equation in vertex form.

3, 8