Chapter 9 Review II

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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

+ 5 (0.589, 5.59) and (3.41, 8.41)