Warm Up

Find five points and use them to graph

Hint, use an x-y table to help you

2y x

11-1 Graphing Quadratic Functions

Objective: To find and use the axis of symmetry and the vertex of a parabola to graph it.

Standard 21.0

Graph for Warm Up

This “U” shape is called a parabola.

Quadratic Function: y = Ax2 + Bx + CA,B,C are integers

Axis of SymmetryCuts parabola in halfReflects over linex = 0

VertexTurning point(0,0)On axis of symmetry

Magic Ordered Pairs(1,1a) (2,4a) (3,9a)

Use these every timeWhen A,B,C change,

moves vertex but does not change the shape

2

bx

a

Looks like..

A parabola can also make shape.

To tell which way it points, look at the a value

a (+) = + + minimum (vertex)

A (-) = – – maximum (vertex)

2y ax bx c

ExamplesStandard Form

Opens Up or Down

Find the axis of

symmetry

Find the

vertex

Graph using the parent function

y = ax2 + bx + ca(+) = up/mina(-) = down/maxx = – b

2a

Plug in x to standard form

(1,1) (2,4)(3,9) reflect

y = x2

“Parent function”

y = 1x2 + 0x + 0

a = 1b = 0c = 0

Up

VertexMinimum

x = 0 2(1)

x = 0

y = (0)2

y = 0

(0,0) This is the same graph as the

warm up!

“11-1 Graphing Quadratic Functions” Worksheet

Follow along and fill in the worksheet with me.

We will graph 3 parabolas today in class You will complete tonight’s homework on a

similar worksheet so… Take good notes in class so you can use them to

help you do the homework!

HOMEWORK See problems below:

1) y = x2 + 4x + 32) y = -x2 + 4x – 13) y = x2 + 6x + 9 4) y = -x2 – 35) y = x2 – 4x

To be done on worksheet given in class Answers include: Up/down?

Min/Max?Axis of SymmetryVertexGraph

Extra Practice!

The following 2 parabolas can be graphed and studied for extra practice

ExamplesStandard Form

Opens Up or Down

Find the axis of

symmetry

Find the

vertex

Graph using the parent function

ax2 + bx + c = ya(+) = upa(-) = down x = – b

2a

Plug in x to standard form

(1,1) (2,4)(3,9) reflect

y = x2 – 2x – 3

y = x2 – 2x – 3

a = 1b = -2c = -3

Up

VertexMinimum

x = -(-2) 2(1)

x = 1

y = (1)2 – 2(1) – 3 y = 1 – 2 – 3 y = -4

(1,-4)

ExamplesStandard Form

Opens Up or Down

Find the axis of

symmetry

Find the

vertex

Graph using the parent function

ax2 + bx + c = ya(+) = upa(-) = down x = – b

2a

Plug in x to standard form

(1,1) (2,4)(3,9) reflect

y = x2 + 4x + 4

y = x2 + 4x + 4

a = 1b = 4c = 4

Up

VertexMinimum

x = -(4) 2(1)

x = -2

y = (-2)2 + 4(-2) + 4 y = 4 – 8 +4 y = 0

(-2,0)