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

Use the complete the square formula. \[{a(x+D)}^{2}+E\]
−4x^2 + 24x − 29 is ax^2 + bx + c.
a = -4, b = 24, and c = -29.

Find D.
\[D=\frac{b}{2a}=\frac{24}{2\times -4}\]

Then, find E.
\[E=c-\frac{{b}^{2}}{4a}=-29-\frac{{24}^{2}}{4\times -4}\]

Once you've found D and E, plug them into the complete the square formula. \[{a(x+D)}^{2}+E\]

Answer 2

Thanks