Math In Basketball Lesson Page 20
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31Answer Key
Math in Basketball: Take the challenge
Strategy B:
Another option is to graph the equation for the height of the ball, either using a graphing calculator or paper
and pencil with a table of values. Then, you can use your graph to estimate the values of t at which the ball
reaches 10 feet.
3. Solve your problem. Show all your steps. You may use the graph on the last page or show
your work in the space below.
Strategy A:
√
• Use the quadratic formula:
=
t
0.14 or 1.36
• Complete the square:
2
h(t) = -16t
+ 24t + 7
2
10 = -16t
+ 24t + 7
2
3 = -16t
+ 24t
2
3 = -16(t
+ t)
2
= (t
+ t)
+
2
2
2
(- )
= t
+ t +( *
)
2
= (t - )
√
1.36 or 0.14
t
=
Strategy B: See last page of this answer key for sample graph.
Your solution: (Round your answer to the nearest hundredth.)
• The time(s) the ball will reach 10 feet are:
0.14 and 1.36 seconds
AT WHAT TIME DOES THE BALL REACH THE MAXIMUM HEIGHT?
4. Plan it out. What strategy will you use? Select one or more representations, such as your
equation or a graph (found on the last page), to calculate the value(s) of
t
when the ball
reaches its maximum height.
Strategy A:
Represented graphically, the equation for height as a function of time, or h(t), is a parabola. Like all
parabolas, it is symmetrical, meaning that it has an axis of symmetry that passes through the vertex, or
highest point. Since you now know the two values of t when the ball reaches a height of 10 feet, you can
find the axis of symmetry by calculating the halfway point, or mean, between these two times. This will
give you the value of t when the ball reaches its maximum height.
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