Chapter 9 Review II

Report
For f(x) = x2 – 3x – 15 find f(-2)
-5
Determine the vertex, axis of symmetry and
graph.
2
y  x 3
Vertex: (0, 3)
Axis of
symmetry:
x=0
x
y
-2
-1
7
4
0
1
2
3
4
7
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
12
minimize the cost of production?
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.
P=2L+ 2w
200 = 2L + 2x
Area = x(100 – x)
Area = 100x – x2
100 – x = L
The vertex is:
100 – x
(50, 2500)
x
The maximum area is
2500cm2.
Find the minimum of
f(x) = 2x2 – 6x + 5
x
b
2a

6
2(2)

6
2

3
2
2
1
3
3
3
f    2   6   5 
2
2
2
2
3 1
 , 
2 2
State the vertex, equation for the axis of
symmetry, y-intercept.
y  2 ( x  1)  3
2
Vertex: (1, -3)
Axis of symmetry: x = 1
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 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 = x2 + 8x + 11
Vertex: (-4, -5)
Axis of symmetry:
x = -4
x
y
-6
-5
-1
-4
-4
-3
-2
-5
-4
-1
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?
t = 10 seconds
b) What is the maximum height reached by the
H(10) = 500 meters
rocket?
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) = -x2 + 50x – 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= x2 – 3x + 7 and y = x + 5
(0.589, 5.59) and
(3.41, 8.41)

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