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.
The path of the water is −4(x − 3)2 + 7 and the maximum height of the water is 7 feet. Then the correct option is C.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The height of water shooting from a fountain is modeled by the function given below.
f(x) = −4x² + 24x − 29, where x is the distance from the spout in feet.
Then the quadratic equation is converted into the square form. Then the equation will be
f(x) = −4x² + 24x − 29 - 7 + 7
f(x) = −4x² + 24x − 36 + 7
f(x) = −4(x² - 6x + 9) + 7
f(x) = −4(x - 3)² + 7
The maximum height of the parabola is 7.
The path of the water is −4(x − 3)2 + 7 and the maximum height of the water is 7 feet.
Then the correct option is C.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
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