Question

The Buckingham Fountain in Chicago shoots water from a nozzle at the base of the fountain. The height h, in feet, of the water above the ground t seconds after it leaves the nozzle is given by the function h(t) = –16t2 + 90t + 15. What is the maximum height of the water? Round to the nearest tenth.

Answer 1

I urge you to learn to follow simple directions before you try anything more complicated.

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Answer 2

you know that the vertex of the parabola

y = ax^2+bx+c is at x = -b/2a.

So, your maximum height is at t = 90/32
Just find h(90/32)

Or, rewrite the equation by completing the square:

h(t) = –16t^2 + 90t + 15
= -16(t^2-90/16 t) + 15
= -16(t^2 - 90/16t + (90/32))^2 + 15 + 16(90/32)^2
= -16(t - 90/32)^2 + 2265/16

So, clearly the max height, reached at t = 90/32, is 2265/16