(2) ­ Graphing Quadratic Function in Vertex Form.notebook February 10, 2015

Vertex:

Graph y = -2x2 + 4x + 5

AOS:

D:

R:

y-int:

Bell Work

1.2 Graphing Quadratic Functions in Vertex Form

In section 1.1 we graphed quadratic functions in standard form.y = ax2 + bx + c

Today we will be graphing quadratic functions in vertex form.

y = a(x - h)2 + k

(2) ­ Graphing Quadratic Function in Vertex Form.notebook February 10, 2015

Graph the following on your calculator. Find the following characteristics.

1. y = -2(x + 3)2 - 4

2. f(x) = 2(x - 1)2 + 4

3. y = -(x + 2)2 + 7

4. f(x) = (x - 4)2 - 3 23

VertexAxis of

SymmetryOpens Up or Down?

y = a(x - h)2 + kVertical

Stretch or Compression?

32

1. y = -2(x + 3)2 - 4

2. f(x) = 2(x - 1)2 + 4

3. y = -(x + 2)2 + 7

4. f(x) = (x - 4)2 - 3

Based on your findings, can you state what the vertex and axis of symmetry will be for all quadratics in vertex

form?

Vertex: (h,k)

Axis of Symmetry: x =h

How do you know if the parabola opens up or down?- If a is positive, the parabola opens up.- If a is negative, the parabola opens down.

y = a(x - h)2 + k

How do you know if the parabola is a vertical stretch or shrink?

If a > 1 there is a vertical stretch. If a < 1 there is a vertical shrink/compression.

____ __

__

(2) ­ Graphing Quadratic Function in Vertex Form.notebook February 10, 2015

Compare to the Parent:

Axis of Symmetry:

Vertex:

D:

R:

R:

Graph y = -(x+5)2+2

Writing a Quadratic Function in Vertex Form

Write y = x2 - 10x + 22 in vertex form.

Write y = x2 - 8x + 7 in vertex form.

(2) ­ Graphing Quadratic Function in Vertex Form.notebook February 10, 2015

Writing a Quadratic Function in Vertex Form

Example: Write y = 2x2 + 12x + 6 in vertex form.

Try This: Write y = 3x2 - 12x - 12 in vertex form.

Vertex:

Axis of Symmetry:

D:

R:

Compare toparent:

Graph f(x) = x2 + 2x - 7

(2) ­ Graphing Quadratic Function in Vertex Form.notebook February 10, 2015

Graph f(x) = 1/2 (x + 2)2 - 3

Vertex:

Axis of Symmetry:

D:R:

Compare toparent:

Vertex:

Axis of Symmetry:

D:R:

Compare toparent:

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

(2) ­ Graphing Quadratic Function in Vertex Form.notebook February 10, 2015

The Tacoma Narrows Bridge in Washington has two towers that each rise 307 feet above the roadway and are connected by suspension cables as shown. Each cable can be modeled by the function y = 1/7000 (x - 1400)2 + 27, where x and y are measured in feet. Find the distance between the two towers.

The function y = -0.03(x - 14)2 + 6 models the jump of a red kangaroo where x is the horizontal distance in feet and y is the corresponding height in feet. What is the kangaroo's maximum height? How long is the kangaroo's jump?

(2) ­ Graphing Quadratic Function in Vertex Form.notebook February 10, 2015

Assignment:

p. 15 # 4, 6, 8, 10, 52

On all graphs, find the following:

• Vertex

• Axis of Symmetry

• Compare to Parent Function

• Domain

• Range