# GOLF QUADRATICS!

### With The Great Wasif & Noah

The height *h* (in feet) above the ground of a golf ball depends on the time, *t* (in seconds) it has been in the air. Earl hits a shot off the tee that has a height modeled by the function F(t)= -16t^2 + 100t. Round answers to the nearest hundredth when necessary.

**Time is the independent and the height is the dependent**

3. What is a reasonable domain and range for this function?

**Domain= all real numbers**

**Range = y < 156**

4. How long is the golf ball in the air?

**The golf ball is in the air for for 6.3 seconds**

## Questions #5-8: Show graphically.

5. What is the maximum height of the ball?

**156.25ft**

6. How long after it is hit does the golf ball reach the maximum height?

**After 3.125 seconds**

7. What is the height of the ball at 3.5 seconds? Is there another time at which the ball is at this same height? If so, when?

**154 ft after 3.5 seconds, it is also this height at 2.75 seconds**

8. At approximately what time is the ball 65 feet in the air? Explain.

**At 0.737 seconds it reaches 65 feet in the air, and at approximately 5.5131 seconds it reached this height while falling.**

9. Tweety Bird takes off from the green at the same time you tee off. His height is increasing at a rate of 4 feet per second. When will he be at the same height as your ball? What is that height? Graph this scenario.

**In 6 seconds he reaches the same height as the ball at 24 ft in the air.**

10. Suppose Gloria and Earl stand side by side and teed off at the same time. The height of Gloria’s ball is modeled by the function F(t)= -16t^2 + 80t. Earl hits a shot off the tee that has a height modeled by the function F(t)= -16t^2 + 100t. Whose golf ball will hit the ground first? How much sooner does it hit the ground? How high will Gloria’s ball go? Compare the two shots graphically.

**Gloria’s ball hits the ground 1.25 seconds before Earls ball, but Glorias ball goes up a 100ft, while earls goes a 156.25ft.**

11. Suppose the Earl hit a second ball from a tee that was elevated 20 feet above the fairway.

*a. What effect would the change in elevation have on the graph? *

**The ball would go 20ft higher in the same amount of time, but it would take longer to land on the ground**

*b. Write a function that describes the new path of the ball.*

**F(t)= -16t^2 + 100t + 20**

*c. Graph the new relationship between height and time. Make sure to label the graph and to graph the original function as well as the new function in the given graph.*

**Picture below**

*d. What would be a reasonable domain and range of this new function?*

**D= All real numbers**

**R= y < 176.25**