Warm-up (10-25-11)

• 1. Multiply with FOIL (2x – 4)(6x – 2)

• 2. Given y = -2(x – 4)2 + 5, then finda. Vertex Point?

b. AOS?

c. y-intercept?

d. Opening Direction?

e. Graph it?

212 28 8x x

(4,5)

4x (0, 27)

Down

Chapter 4

Section 4-1

Graphing Quadratic Equations

Objectives

• I can identify a, b, c from a quadratic equation

• I can graph Quadratic Functions manually with Data Table, including Axis of Symmetry

• I can describe the three types of solutions to a quadratic equation

Quadratic Equation

• A quadratic equation is an equation that can be written in the format

• y = ax2 + bx + c, where a 0

• ax2 is the quadratic term that makes it a quadratic

Real World Applications

Vocabulary versus Answer Format

• Solutions and Roots have the same answer format:x = or in braces {}

x = 3, 5 {3, 5}

• Zeros and x-intercepts have the same answer format as ordered pairs

• (xint , 0)

• (3, 0) and (5, 0)

Axis of Symmetry

• The axis of symmetry can be found by the following equation:

a

bx

2

y = 3x2 - 2x - 1

• Find AOS?

• a = 3, b = -2, c = -1

• AOS:

2

bx

a

( 2)

2(3)x

2

6x

1

3x

y = -2x2 + 4x - 8

• Find AOS?

• a = -2, b = 4, c = -8

• AOS:

2

bx

a

4

2( 2)x

4

4x

1x

Finding the Vertex Point

• If the AOS is x = 1, then the Vertex Point is Vertex (1, ?)

• How can I find the y-value?

• PLUG the x-value back into the equation for all x’s and solve for “y”

y = -2x2 + 4x - 8

• AOS: x = 1

• Now use this x-value to find the vertex point

• y = -2(1)2 + 4(1) – 8

• y = -2 + 4 – 8

• y = -6

• Vertex (1, -6)

Putting it ALL together to GRAPH

2Given the quadratic: y ax bx c

1. Find AOS with formula: 2

bx

a

2. Find Vertex Point using x-value

and plugging into equation

3. Make a data table and find other points

Example

• Let’s graph y = 2x2 + 4x – 5

• So we need:

• 1. AOS

• 2. Vertex Point

• 3. More points to graph

Homework

• Worksheet 4-2