# Golf Algebra Project

### GOLF GOLF GOLF

## 1.

**Graph this function **f*(t) = -16t**2** + 100t*

## 2.

**What are the independent and dependent variables in this situation?**

Independent: Time (x or t) Dependent: Height (y or f(t))

## 3.

**What is a reasonable domain and range for this function?**

**Domain** - all reals, **range** - y ≤156.25

## 4.

**How long is the golf ball in the air? **

6.25 seconds

## 5.

** What is the maximum height of the ball?**

156.25 feet

## 6.

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

3.13 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?**

At 3.5 seconds, the ball is at 154 ft . The ball is also at the same height at 2.5 seconds.

## 8.

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

** **

0.74/0.75 seconds. We calculated using G-solve (x-cal)

## 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.**

He will be at the same height as the ball at 6 seconds and 24 feet 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 will hit the ground at 5 seconds , and it will reach 100 feet in altitude. It will also be 1.25 seconds faster than Earl's ball.

Red is Gloria, Green is Earl.

## 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? __

It would increase the elevation by a significant amount.

__b. Write a function that describes the new path of the ball. __

f(x) = -16x*2** + 120x *

__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. __

Time doesn’t change, it does not increase or decrease. Only the air altitude increases, from the maximum being 156.25 feet, to 225 feet.

## Original Trajectory (Earl) This is the original height of the ball. | | ## Earl's is higher now See how the green ball was lifted up higher? The new path's equation is: f(x) = -16x 2 + 120x |

__d. What would be a reasonable domain and range of this new function?__

Domain- x= all reals Range- y≤ 225