A golf ball is hit, and it leands at a point on the same horizontal plane 53 m away. The path of the ball took it just over a 9-m-tall tree that was 8 m in front of the golfer.
a) Assume the ball is hit from the origin of a coordinate plane. Find a quadratic function that describes the path of the ball.
b) What is the maximum height of the ball?
c) It is possible to move the origin in this situation and develop another quadratic function to describe the path? If so, find a second quadratic function.

Use the same method as in this post.

https://www.askmehelpdesk.com/mathematics/representing-given-information-quadratic-function-517967.html

Another way to aproach these is to use:

y=a(x-h)^{2}+k

Where (h,k) is the coordinates of the vertex, or the max height of the ball.

The top of the fence is at (8,9)

and the landing point is at (53,0)

We know the max height horizontal distance occurs at 26.5

9=a(8-\frac{53}{2})^{2}+k

0=a(53-\frac{53}{2})^{2}+k

Using these two equations and solving for a and k, we get

a=\frac{-1}{40}

Which means k=\frac{2809}{160}

y=\frac{-1}{40}(x-\frac{53}{2})^{2}+\frac{2809}{160}