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