#### Transcript Chapter 9 Review II

For

*f(x) *

=

*x*

2 – 3

*x*

– 15 find

*f(*

-2

*)*

-5

**Determine the vertex, axis of symmetry and graph.**

*y*

*x*

2 3 Vertex:

**(0, 3)**

Axis of symmetry:

**x = 0**

x

**-2 -1 0 1 2 7 4 3 4 7**

y

Find the vertex and axes intercepts.

*y*

### = -3

*x*

2

### - 6

*x*

### Vertex:

**(-1, 3)**

### y-intercept: (0, 0) x-intercepts:

**(-2, 0) & (0, 0)**

Find the coordinates of the points of intersection of the graphs with equations

*y*

=

*x*

2 – 5

*x*

+ 10 and

*y*

=

*x *

+ 5

## (1, 6) and (5, 10)

A skateboard manufacturer finds that the cost $C of making x skateboards per day is given by

*C(x) *

=

*x*

2 – 24

*x*

+ 244 a) How many skateboards should be made per day to minimize the cost of production?

12 b) What is the minimum cost?

$100

A rectangular has a perimeter of 200cm. Let

*x*

be the width of the rectangle. Find the maximum area for the rectangle.

Area =

*x*

(100 –

*x*

) P=2L+ 2w 200 = 2L + 2x Area = 100

*x*

–

*x*

2 100 – x = L The vertex is: (50, 2500) 100 – x x The maximum area is 2500cm 2 .

Find the minimum of

*f(x) *

= 2

*x*

2 – 6

*x*

+ 5

*x*

*b*

2

*a*

6 2 ( 2 ) 6 2 3 2

*f*

3 2 2 3 2 2 6 3 2 5 1 2 3 2 , 1 2

State the vertex, equation for the axis of symmetry,

*y*

-intercept.

*y*

2 (

*x*

1 ) 2 3 Vertex:

**(1, -3)**

Axis of symmetry:

**x = 1**

y-intercept:

**(0, -1)**

Determine the axis of symmetry and vertex.

*y*

=

*x*

2 – 4

*x*

+ 7 Vertex:

**(2, 3)**

Axis of symmetry:

*x *= 2

For

*y*

=

*x*

2 – 2

*x*

• axes intercepts find the • direction the parabola opens • equation of the axis of symmetry and graph Opens up

*y*

-intercept:

**(0, 0)**

*x*

-intercepts:

**(0, 0) & (2, 0)**

Vertex:

**(1, -1)**

Axis of symmetry:

*x *= 1

Name the vertex and axis of symmetry. Graph.

*y*

### =

*x*

2

### + 8

*x *

### + 11

Vertex:

**(-4, -5)**

Axis of symmetry:

*x *= -4

x

**-6 -5 -4 -3 -2 -1 -4 -5 -4 -1**

y

Name the vertex and axis of symmetry.

*y*

### =

*x*

2

### – 7

Vertex:

**(0, -7)**

Axis of symmetry:

*x *= 0

A manufacturer of barbeques knows that if

*x*

of them are made each week then the total cost will be (60

*x*

+ 800) dollars and the total receipts per week will be (1000

*x*

– 3

*x*

2 ) dollars. How many barbeques should be made per week for maximum profits?

157

*t*

The height 0.

*H*

meters, of a rocket

*t*

seconds after it is fired vertically upwards is given by

*H*

(

*t*

) = 100

*t*

– 5

*t*

2 , a) How long does it take for the rocket to reach its maximum height?

*t *= 10 seconds

b) What is the maximum height reached by the rocket?

*H*(10) = 500 meters

c) How long does it take for the rocket to fall back to earth?

**20 seconds**

A manufacturer finds that the profit $P from assembling

*x*

bicycles per day is given by P(

*x*

) = -

*x*

2 + 50

*x*

– 200.

a) How many bicycles should be assembled per day to maximize the profit?

**25 bicycles**

b) What is the maximum profit?

**$425**

c) What is the loss made if no bicycles are assembled in a day?

**$200**

Find the coordinates of the points of intersection of the graphs with equations

*y*

### =

*x*

2

### – 3

*x*

### + 7 and

*y*

### =

*x*