The path of a ping pong ball that is hit from one end of the table can be modeled by the equation (y = - 1/4 x^2 5x) where x is measured in inches and represents the horizontal distance from the edge of the table, and y represents the height of the ping pong ball in inches above the table. What is the maximum height of the ping pong ball?

A.

The ball reaches a maximum height of 30 inches above the table.

B.

The ball reaches a maximum height of 20 inches above the table.

C.

The ball reaches a maximum height of 25 inches above the table.

D.

The ball reaches a maximum height of 27 inches above the table.

There is something missing in the given model equation. I think the correct equation is y = - 1/4 x^2 + 5x. You maybe forgot to type the '+' sign. I checked it initially, and I got an answer that's in the choices. So, hopefully, this is correct.

To find the maximum height, you must solve this equation through differential calculus. To find the maxima or minima, you differentiate the equation y in terms of x and equate it to zero.

y' = 2 (-1/4) x + 5 = - 1/2*x + 5 = 0

By doing this, you would solve the value of x or the horizontal distance.

-1/2*x = - 5

x = - 5*-2

x = 10 inches

Finally, we substitute this x to the original equation to determine the maximum height y.

y = - 1/4*10 + 5 (10)

y = 25 inches

The answer is C.