y ax2 bx c

Quadratic Equation (Standard Form)

Quadratic Term

Linear Term

Constant Term

y 2x2 3x 5

5.1 Graphing Quadratic Function, p. 249Objective: To Graph Quadratic Functions

x

yGraph

2y x

x y0

1

−1

2−2

±3

01

1

44

9

Vertex

Axis (Line) of Symmetry

2y x

5.1 Graphing Quadratic Function, p. 249Objective: To Graph Quadratic Functions

x

yGraph 2y x

x y0

1

−1

2−2

±3

0−1

−1

−4−4

−9

2y x

2y x

5.1 Graphing Quadratic Function, p. 249Objective: To Graph Quadratic Functions

Using your Graphing Calculator:• Y = where you type in the

function you want to graph• WINDOW sets the size of your

screen (x and y axis)• ZOOM lets you see a closer look• TRACE shows coordinates of

points on screen• GRAPH graphs the function in Y=

y ax2 bx cQuadratic Equation

Quadratic Term

Constant Term

a+a opens up−a opens down

skinny parabola a  1

wide parabola0  a  1

c

+c shifts up−c shifts down

y-intercept

(fraction)

5.1 Graphing Quadratic Function, p. 249Objective: To Graph Quadratic Functions

x

y

Graph y

1

2(x 3)2 1

1. Vertex (3, 1)

2. Axis of Symmetry

                      3 x3.  Find Points

x y

1 3 0 5.5

Vertex Form

x

y

2Graph ) 2( 5y x

1. Vertex ( )5, 2

2. Axis of Symmetry

                      5 x 3.  Find Points

x y

-4 1 -3 -2

Vertex Form

Write in standard form.

1)

2)

y (x 5)(x 6)

y (x 3)(x 7)

y x2 6x 5x 30

y x2 x 30

y (x2  3x 7x 21)

y x2 4x 21

Write in standard form.

1)

2)

y 2(x 1)2 3

y 3(x 2)2 5

y 2(x 1)(x 1) 3y 2(x2 2x 1) 3y 2x2 4x 2 3y 2x2 4x 5

y 3(x2 4x 4) 5y 3x2 12x 12 5y 3x2 12x 7

y a(x h)2 k

Vertex Form of a Quadratic Equation

        vertex ( , )

axis of symmetry

h k

x h

Intercept Form of a Quadratic Equation

y a(x p)(x q)

-intercepts are  and x p q

Axis of Symmetry is halfway

  between ( , 0) and ( , 0).p qp