Relating The Standard And Factored Forms Worksheet - Chapter 3.2 Page 5
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1
2
3
4
5
6
7
8
9
10
114 1 (21.5)
I used the zeros to find the axis of
x 5
symmetry. I know that the axis of
2
symmetry is halfway between the
2.5
x 5
zeros. I added the two zeros and
2
divided by 2.
x 5 1.25
The equation of the axis of symmetry is
x 5 1.25.
x 5 1.25
f (1.25) 5 2(1.25)
2 5(1.25) 2 12
2
I put
into the original
function and solved to get the
5 3.125 2 6.25 2 12
y-coordinate of the vertex.
5 215.125
The vertex is (1.25, 215.125).
f(x)
4
x
I used the values I calculated to
2 0
4
2
4
6
draw the graph of a parabola. It
4
a . 0.
opens up, since
8
(1.25, 215.125).
The vertex is
12
The zeros are (4, 0) and
(21.5, 0).
16
The y-intercept is (0, 212).
3
Solving problems using a quadratic
EXAMPLE
function model
The height of a football kicked from the ground is given by the function
h(t) 5 25t
1 20t,
2
where h(t) is the height in metres and t is the time in
seconds from its release.
a) Write the function in factored form.
b) When will the football hit the ground?
c) When will the football reach its maximum height?
d) What is the maximum height the football reaches?
e) Graph the height of the football in terms of time without using a table of values.
Matt’s Solution
h(t) 5 25t
1 20t
I wrote the function in factored
2
a)
form by dividing out the common
h(t) 5 25t(t 2 4)
factor 25t.
136
Chapter 3
NEL
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