Question 253303
{{{y = -2x^2+12x}}}
The maximum height of this parabola will be found at its vertex, so let's find out where the vertex is:
The x-coordinate of the vertex is given by:
{{{x = (-b)/2a}}} where: a = -2 and b = 12, so...
{{{x = (-12)/2(-2)}}}
{{{x = 12/4}}}
{{{x = 3}}} Now substitute this value of x into the original equation to find the y-coordinate of the vertex and, this of course, corresponds to the maximum height of the arch in your problem.
{{{y = -2x^2+12x}}} Substitute x = 3.
{{{y = -2(3)^2+12(3)}}}
{{{y = -18+36}}}
{{{highlight(y = 18)}}}feet. This is the maximum height of the arch.