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.

f(x)=−4(x2−6x+9−9)−29

 (x2−6x+9)=(x−3)(x−3)

f(x)=−4((x−3)2−9)−29

f(x)=−4(x−3)2−4(−9)−29

f(x)=−4(x−3)2+36−29

f(x=−4(x−3)2+7

f(x)=−4(x−3)2+7

That's the equation we got by completing the square.

y=a(x−h)2+k

That's the formula of a parabola in "vertex" form. Notice the similarity? The two are equal if we say

y=f(x)

a=−4

h=3

k=7

Therefore the answer is C, −4(x − 3)2 + 7; The maximum height of the water is 7 feet.

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