anonymous one year ago 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.

1. anonymous

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. ${a(x+D)}^{2}+E$

2. anonymous

Thanks