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.

Question

surjithayer · Answer

do you know how to solve it?

angelcook2007 · Answer

no

surjithayer · Answer

$$f(x)=-4x^2+24x-29$$
$$=-4(x^2-6x+...)-29$$
can you complete the square?

surjithayer · Answer

$$=-4[x^2-6x+{(coefficient~of~x)/2)}^2-((coefficient ~of~x)/2)^2]-29$$

angelcook2007 · Answer

I got it, thanks mate

surjithayer · Answer

$$=-4(x^2-6x+(-6/2)^2-(-6/2)^2)-29$$
$$=-4(x-3)^2-4(-9)-29$$
$$=-4(x-3)^2+36-29$$
$$=-4(x-3)^2+7$$
so maximum height of water=7 ft.

angelcook2007 · Answer

Thank you, I ended up making a 100