For f(x) = x2 – 3x – 15 find f(-2)

-5

y x 2 3

x y

0 3

-1 4

1 4

-2 7

2 7

Vertex: (0, 3)

Axis of symmetry:

x = 0

Determine the vertex, axis of symmetry and graph.

Find the vertex and axes intercepts.

y = -3x2 - 6x

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 = x2 – 5x + 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) = x2 – 24x + 244

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

b) What is the minimum cost?

12

$100

A rectangular has a perimeter of 200cm. Let x be the width of the rectangle. Find the maximum area for the rectangle.

x

Area = x(100 – x)

Area = 100x – x2

100 – xThe vertex is:

The maximum area is 2500cm2.

(50, 2500)

P=2L+ 2w200 = 2L + 2x

100 – x = L

2

3

2

6

)2(2

6

2

a

bx

2

1,

2

3

2

15

2

36

2

32

2

32

f

Find the minimum of f(x) = 2x2 – 6x + 5

Vertex: (1, -3)

Axis of symmetry: x = 1

3)1(2 2 xy

State the vertex, equation for the axis of symmetry, y-intercept.

y-intercept: (0, -1)

Determine the axis of symmetry and vertex.

y = x2 – 4x + 7

Vertex: (2, 3)

Axis of symmetry: x = 2

For y = x2 – 2x find the • direction the parabola opens• axes intercepts• equation of the axis of symmetryand graph

Opens upy-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 = x2 + 8x + 11

x y

-4 -5

-5 -4

-3 -4

-6 -1

-2 -1

Vertex: (-4, -5)Axis of symmetry:

x = -4

Name the vertex and axis of symmetry.

y = x2 – 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 (60x + 800) dollars and the total receipts per week will be (1000x – 3x2) dollars.

How many barbeques should be made per week for maximum profits?

157

The height H meters, of a rocket t seconds after it is fired vertically upwards is given by H(t) = 100t – 5t2, t 0.a) How long does it take for the rocket to reach its

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

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

earth?

t = 10 seconds

H(10) = 500 meters

20 seconds

A manufacturer finds that the profit $P from assembling x bicycles per day is given by P(x) = -x2 + 50x – 200.

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

b) What is the maximum profit?

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

25 bicycles

$425

$200

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

y= x2 – 3x + 7 and y = x + 5

(0.589, 5.59) and (3.41, 8.41)