Chapter 5.7/Day 2Quadratic Functions in Vertex FormTarget Goals: 1. Write/graph equations in vertex form2. Identify the vertex, axis of symmetry, and direction of opening.

OPENER/REVIEWGraph the function

• y-intercept:

• Axis of symmetry:

• Vertex:

• Direction of opening:

2( ) 5f x x

2(0) 0 5f 5

2bxa

02(1)

0

2(0) 0 5f 5

UP

2(2) 2 5f 1

2 Forms for Quadratic Functions

Quadratic Form Vertex Form2( )f x ax bx c 2( )f x a x h k

Yesterday

TODAY!!!

VERTEX FORM:

AXIS of SYMMETRY:

VERTEX:

2( )f x a x h k

x h

(h, k)

DIRECTION of OPENING:

If a is +, then opens UP.If a is -, then opens DOWN.

Ex 1) Graph using vertex form: 23 2y x

Vertex: (3, -2)

A.O.S.: x = 3

Direction:

UP!

22 3 2y 21 2y 1 2 1y (2, 1)

Ex 2) Graph using vertex form. 22 3 1y x

Vertex: (-3, 1)

A.O.S.: x = -3

Direction:

DOWN!

22 2 3 1y

1y

( 2, 1)

Ex 3) Which is an equation of the function shown in the graph?A.

B.

C.

D.

24 3 2y x

21 3 24

y x

21 3 24

y x

24 3 2y x

Vertex?

(3, 2)

2y a x h k 23 2y a x

21 1 3 2a 1 4 2a 1 4a 14

a

Opens?

DOWN

Ex 4) APPLICATION!•During an Independence Day fireworks

show, the height h in meters of a specific rocket after t seconds can be modeled by

•What is the maximum height of the rocket?

•What is the time when this maximum height occurs?

2( ) 4.9 4 80h t t

“Fist of 5”

1 5

Target Goals Accomplished?•“Write/graph equations in vertex form.”

▫Ex’s 1, 2, 3, 4, 5 •“Identify the vertex, axis of symmetry, and

direction of opening.”▫Ex’s 1, 2, 3, 4, 5

•HW – page 308 #4, 5, 7, 22, 24-26, 29-31, 33, 35, 37, 63-65