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.
