Question

The shape of a supporting arch can be modeled by h(x)= -0.03^2+3x, where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch.

Answer 1

You probably meant h(x)= -0.03x^2+3x

several ways to do this
1. by Calculus, find derivative, set it equal to zero and solve

2. by completing the square and changing the equation to the standard form of a parabola

3. in this case this is the easiest way:
since it factors to

h(x)= x(-0.03x+3)

and when h(x) = 0, x = 0 or -.03x+3=0
yielding x = 100

so the x-intercept of this parabola are 0 and 100, which means that the vertex is at the midway, or at x=50

so h(50) = 75