Today’s Date:

1/17/12

7.5 Vertex Form of Quadratic

Vertex Form

2y ax bx c Standard Form:

Vertex Form: 2( )y a x h k

( , )V h k

Find the Vertex

Inside Parenthesis → Opp. Sign

(3,7)V

Outside Parenthesis → Same Sign

2y x

2( 3) 7y x

2 1y x

2( 0) 0y x (0,0)V

2( 0) 1y x (0,1)V

Ex 1)

Ex 2)

Ex 3)

Ex 4) Graph 22( 3) 5y x

1) Which way does it open? Wide or skinny?“a” = (–) – opens DOWN│-2│> 1 → skinny

3) (A of S): 3x

2) Vertex: ( 3,5)

4) MAX or MIN? MAX5) Extreme value: 5 (y part of vertex)

Ex 4 cont…

6) x-int: 7) y-int:( , 0)20 2( 3) 5x

22( 3) 5y x

25 2( 3)x 25

( 3)2

x

53

2x

22(0 3) 5y 2(9) 5 13

53

2x

103

2x

103 ,0

2

(0, 13)

Ex 4 cont…

9) GraphUse the A of SNormal: Right 1 Up 1 a = -2: Right 1 Down 2

Left 1 Down 2From Vertex (-3, 5)

Converting SF → VF

Complete the Square!!

2y ax bx c 2( )y a x h k

23 6 12y x x 212 3 6y x x 212 3( 2 )y x x 13(1)

29 3( 1)y x 23( 1) 9y x

Vertex? ( 1,9) Extreme Value? 9

Move constant

Factor out coeff on x2

Cut middle term in half & square it → Add to both sides of

=CAREFUL!!! Added 3(1) not 1!!

Move constant back over

Write as perfect square

Ex 5)

Convert to Vertex Form

24 2y x x 22 4y x x

22( 2 )y x x 1( 2)(1) 22 2( 1)y x

22( 1) 2y x

Vertex? (1,2)

Extreme Value? 2

Ex 6)

Homework

#709

Pg. 330 Oral Ex. 1 – 14

Pg. 336 (Directions: SF → VF & ID Vertex & Extreme Value)

7, 9, 11, 14, 15