Question

The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29, where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water. −4(x − 3)2 − 29; The maximum height of the water is 3 feet. −4(x − 3)2 − 29; The maximum height of the water is 29 feet. −4(x − 3)2 + 7; The maximum height of the water is 7 feet. −4(x − 3)2 + 7; The maximum height of the water is 3 feet.

Answer 1

Answer:

the maximum height of the water is 7 ft

Step-by-step explanation:

Using " ^ " to indicate exponentiation, we have −4x^2 + 24x − 29.

Rewrite -4x^2 + 24x as -4(x^2 - 6x) and then complete the square of (x^2 - 6x).  We get:

(x^2 - 6x + 9 - 9), which is exactly equivalent to (x^2 - 6x).

Going back to the original equation:  −4x^2 + 24x − 29, or

−4(x^2 - 6x) − 29.

Now replace (x^2 - 6x) with (x^2 - 6x + 9 - 9):

-4(x^2 - 6x + 9 - 9) - 29, which simplifies to:

-4(x - 3)^2 + 36 - 29, or

-4(x - 3)^2 + 7, whose vertex is (3, 7).  Thus, the maximum height of the water is 7 ft.