Question

a fire hose sprays water in an arch that csn be defined by the function. h(x)=-.25x2 +5x where is the horizontal distance from the hose and h(x) is the height of the water.

What is the maximum height of the water and how far does the water reach?

Answer 1

as with all quadratics ax^2+bx+c, the vertex is at x = -b/2a
In this case, that means x = 5/.5 = 10
Since the graph opens downward, the vertex is the maximum value.
So find h(10)
since h(x) = -.25x(x-20), h=0 at x=0 and x=20