Question

The height of water shooting my fountain is modeled by the function f(x)= -4x^2 +24x -29 where x the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water.

Answer 1

To determine the maximum height of the water shooting from the fountain, complete the square of the given function.

Step-by-step explanation:

To determine the maximum height of the water shooting from the fountain, we can complete the square of the given function.

First, the function is in the form f(x) = -4x^2 + 24x - 29.

To complete the square, we need to rewrite the function in the form f(x) = a(x-h)^2 + k.

Using the formula (a/2)^2 = c, where c is the constant term, we have:

f(x) = -4(x^2 - 6x) - 29.

f(x) = -4(x^2 - 6x + 9) - 29 + 4(9).

f(x) = -4(x - 3)^2 + 7.

The maximum height of the water shooting from the fountain is 7 feet, which occurs when x = 3.