Question

Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t^2 + 96t gives the height, in feet, of the soccer ball after t seconds.
1. What are the zeros?

Write the number(s) only. If more than one number exists, separate by a comma.

2. How long will it take for the ball to hit the ground? Write your answer as an integer.

3. What do the x-intercepts represent in this real life situation in regards to the height of the soccer ball at that time?

4. Does this graph have a minimum, maximum or neither?

5. Show ALL work to find the axis of symmetry algebraically.

6. Find the vertex algebraically. Write as an ordered pair.

7. What is the maximum height of the ball? Write your answer as an integer.

8. What does the vertex tell you in regards to the real world example? In other words, when you look at the minimum or maximum on this graph, what does it tell you about the soccer balls path/motion?

9. What is the y-intercept? Write your answer as an ordered pair.

10. What does the y-intercept represent in this real life situation in regards to the height of the soccer ball at that time?

Answer 1

The zeros are the values of t for which f(t) = 0.
i.e. -16t^2 + 96t = 0
16t^2 - 96t = 16t(t - 6)
16t = 0 or t - 6 = 0
t = 0 or t = 6
Therefore, the zeros are 0, 6

The time taken for the ball to hit the ground is the value of t when f(t) = 0.
i.e. t = 6.