Math In Basketball Lesson (Page 24 of 31) in pdf

Math In Basketball Lesson Page 24

Answer Key

Math in Basketball: Try other challenges

Strategy A:

The height (h) of the ball, in feet, at a given time (t) is represented by the equation:

h(t) = -16t

+ v

t + h

[Replace initial vertical velocity and release height values based on selection above.]

The value for t at 10 feet would occur at two points in time, one on the way up, the other at the hoop.

Substitute 10 feet for h(t) and solve.

Write in standard form: 0 = at

+ bt + c by subtracting 10 from each side.

Solve algebraically using the quadratic formula, t =

, or complete the square to find two values

of t.

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 of this

handout or show your work in the space below.

See below for all solutions.

AT WHAT TIME(S) 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

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.

Strategy B:

You can use the properties of the graph of the equation for h(t) to find the value of t for the vertex or

maximum point. For a parabolic function of the form 0 = at

+ bt + c, where a ≠ 0, the value for time (t) is

)

represented by the x-coordinate of the vertex

of the parabola.

5. Solve your problem. Show all your steps. You may use the graph on the last page of this

handout or show your work in the space below.

See below for all solutions.

Math In Basketball Lesson Page 24