Can someone please help me on "The Golf Problem"?!

[space_c0wboy]

Ok, so I've been stuck on this all day and I literally have no idea what to do.

"Use this data to find a function that describes the path of his ball with the height as the dependent variable and horizontal distance as the independent variable. Use this function to answer the follow questions.

Data:
Distance (yds): 0, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Height (yds): 0, 4, 7.5, 14, 20, 24.5, 28, 30.5, 32, 33, 32.5, 31

I tried plugging in the data into the Stat thing or whatever, and then I found the Quadratic regression, and it gave me this equation: y = -.005x^2 + .810x - .006

And these are the questions that came with it:

1. If the green is on the same level as the ball when he hit it and the front of the green is 160 yds. away and the back of the green is 170 yds. away, will the ball land on the green? (Assume he hits the ball straight.)

I get that it's supposed to fall into 160-170, but I don't know how you even arrive at that number. Do you plug something into the function? And is the function is yds.?

2. What is the maximum height of the ball, in feet?

Is this the vertex? And is the function in yards, so I have to convert it?

3. Given the same conditions in #1, will the ball clear a tree that is 35 ft. tall that is 50 yds. in front of the green?

How do I find if it hits something going vertically?

4. Given the same conditions as #1, except that the green is 15 feet above the spot from which he hit the ball, will the ball land on the green?

Please please please help! I've been stuck on this all day!

 

[galactus]

I think there may be a typo in your second row of data. The ball appears to go down, then back up again in mid flight. 30.5, 23, 33?

 

[space_c0wboy]

Sorry! That should be a 32. And on the worksheet itself, it actually does go in that order, so I don't know if that's a typo or something...

Correct data:
Height (yds): 0, 4, 7.5, 14, 20, 24.5, 28, 30.5, 32, 33, 32.5, 31

I think it's saying that it goes up and comes down.

 

[galactus]

I got the same regression as you when rounding.

To find how far it travels when it hits the ground, set your equation equal to 0 and solve for x.

There are 2 values. One for when it is hit and one when it lands.

If your value is between 160 and 170, then it is in the green.

Your equation will give you the info needed. Use it to answer the questions.

It tells you that x is the distance and y is the height at that distance.

#2, yes, the max height is the vertex of the parabola. You can use \(\displaystyle y=c-\frac{b^{2}}{4a}\) to find the max height and \(\displaystyle x=\frac{-b}{2a}\) to find the horizontal distance where it attains its max height.

For #3, draw a picture if necessary. What is x when you are 50 yds on this side of the green. Enter that value into your equation and see if the ball clears the wall. Remember, you equation is in yds and the tree is 35 feet tall. Convert to yds.