A basketball was thrown upward. The basketball’s path is given by the table

Question

d 1 1.5 2 2.5 3 3.5 4 4.5 5

h 3.2 3.55 3.8 3.95 4 3.95 3.8 3.55 3.2

Where h is the basketball’s height, in meters, above the ground and d is the basketball’s horizontal distance, in meters, from where it was thrown.

a) What was the basketball’s greatest height above the ground?

b) What was the basketball’s horizontal distance at this point?

c) On the grid graph the equations that model the path of the ball

d) What was the basketball’s initial height above the ground? (estimate)

Answer 1

a) For the greatest height, you need to look at the data to the right of "h". The greatest value is a height of 4 meters.

b) At a height of 4 meters, this is the fifth entry in the set of data. Thus, to find the corresponding horizontal distance, look for the fifth entry to the right of "d", which is 3 meters.

c) To graph the date on a grid, the d values are on the x axis and the h values are on the y axis. Notice the d values span from 1 to 5, and the h values are between 3 and 4. You should allow for plenty of room on your y axis between 3 and 4, as there are several decimal values between them. Plot the five points (1, 3.2), (1.5, 3.55), all the way to the fifth point (5, 3.2).

d) The points should approximate a parabola, as is the nature of a ball bouncing up and down with the effect of gravity. The initial height occurs at a horizontal distance of zero, which as an estimate would be about 3 meters high. Note that with an upside down parabola such as this, the values increase more quickly, then start to level off at the vertex, which is the maximum height of 4 meters.