Warm UP

• Domain• All real

numbers

• Range• y ≥ -6

• Equation• y = x² -

6

Interval of Increase

0 ≤ x ≤ ∞

Quadratic Form to Form

Notes

Change quadratic functions to standard form

( )( )y = x +1 x +1

+2

2y = x +2x +3

( )2y = x +1 +2 Rewrite (x+1)²

Multiply using FOIL

Combine like terms

2y = x +x +x +1 Don’t forget your +2

2y = ax +bx +c Standard Form

Compare Vertex vs. Standard

Vertex form: ( )2y = a x -h +k Standard form: 2y = ax +bx +c

( )2y = x +1 +2 2y = x +2x +3

a = 1

b = 2

c = 3

You will learn that you will need to identify the values for a, b, and c. Lets get into the habit of identifying them NOW!!

a = 1

h = -1

k = 2

Lets look at our last problem

We converted to

Compare values

Lets try this one!

( )2y = - x +3 +1

Write the quadratic function in standard form. Label the values for a, b, and c.

Steps:

Write (x+3) twice

Multiply using Foil

Distribute the negative

Add the 1 and combine like terms.

Y=-(x+3)(x+3) + 1

Y = -(x² +6x +9) +1

Y= -x² -6x -9 +1

Y = -x² -6x -8

Your Turn

( )2y = 2 x +2

Write the quadratic function in standard form. Label the values for a, b, and c.

( )2y = -2 x +1 +3

Steps:

Write ( ) twice

Mulitply using Foil

Distribute number out front

Combine like terms.

2

2

2

2

2( 2)( 2)

2( 2 2 4)

2 4 4 8

2 4 4 8

2 8 8

x x

x x x

x x x

x x x

y x x

2

2

2

2( 1)( 1) 3

2( 1) 3

2 2 2 2 3

2 4 1

x x

x x x

x x x

y x x

Standard to Vertex 22 8 4y x x

Step 2: Plug x back into equation to get y value

Step 3: change the value of your x

( )2y = a x -h +k

2

bx

a

Step 1: Find x value

Step 4: “a” from standard form is the same “a” in vertex form

82

2(2)x

22( 2) 8( 2) 4y

8 16 4

4

y

y

Vertex: (-2, -4)

2

2

2( ( 2)) ( 4)

2( 2) 4

y x

y x

Steps

Change to standard form

1. FOIL out the ( )

2. Collect like terms

Make sure equation is in y = ax² +bx + c

Y = -2(x-2)(x+3)

3. Distribute

Y = -2 (x² +3x -2x -6)

Y = -2(x² +1x – 6)

Y = -2x² -2x +12

CLASSWORK/HOMEWORK

page 66 (25-27)

Problems on Agenda

Practice Change into Standard

formY = 2(x-4)² + 5

Form?

Vertex

(4, 5)

FOIL

y = 2(x-4)(x-4)

y = 2(x² -4x -4x + 16)

Collect like terms

y = 2(x² -8x + 16)

Distribute

y = 2x² - 16x + 32

Practice Change into standard

formY = 2(x-3)(x+4)

Form?

Intercept

x = 3 x=-4

FOIL

y = 2(x² +4x -3x -12)

Collect like terms

y= 2(x² + 1x -12)

Distribute

y = 2x² + 2x -24