Relating The Standard And Factored Forms Worksheet - Chapter 3.2 Page 11
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1
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8
9
10
11Complete the table.
13.
Axis of
Maximum or
Function in
Function in
Zeros
Symmetry
Minimum Value
Vertex
Factored Form
Standard Form
a)
2 and 8
6
27
22
22
b)
and
21
c)
and 9
5
28
25
d)
and 0
A ball is thrown into water from a cliff that is 175 m high. The height
14.
of the ball above the water after it is thrown is modelled by the
h(t) 5 25t
1 10t 1 175,
2
h(t)
function
where
is the height in
metres and t is time in seconds.
When will the ball reach the water below the cliff?
a)
When will the ball reach a ledge that is 100 m above the water?
b)
The safe stopping distance for a boat travelling at a constant speed in
15.
175 m
d(v) 5
1 10v 1 3000),
2
T
0.002(2v
calm water is given by
where
100 m
d(v) is the distance in metres and v is the speed in kilometres per
hour. What is the initial speed of the boat if it takes 30 m to stop?
f (x) 5 2x
2 4x 2 30
2
Describe how you would sketch the graph of
16.
C
without using a table of values.
Extending
The stainless-steel Gateway Arch in St. Louis, Missouri, is almost
17.
parabolic in shape. It is 192 m from the base of the left leg to the base
of the right leg. The arch is 192 m high. Determine a function, in
standard form, that models the shape of the arch.
A model rocket is shot straight up into the air. The table shows its
18.
height, h(t), at time t. Determine a function, in factored form, that
estimates the height of the rocket at any given time.
Time (s)
0
1
2
3
4
5
6
Height (m)
0.0
25.1
40.4
45.9
41.6
27.5
3.6
The path of a shot put is given by
19.
h(d ) 5
2
20.7d 2 26.28),
where h(d ) is the height
2
0.0502(d
and d is the horizontal distance, both in metres.
h(d ) 5 a(d 2 r) (d 2 s),
Rewrite the relation in the form
a)
where r and s are the zeros of the relation.
What is the significance of r and s in this question?
b)
142
Chapter 3
NEL
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