SOLUTION: An arch is built so that it is 6 feet wide at the base. Its shape can be represented by a parabola with the equation y = -2x2 + 12x, where y is the height of the arch. The maximum

Algebra ->  Circles -> SOLUTION: An arch is built so that it is 6 feet wide at the base. Its shape can be represented by a parabola with the equation y = -2x2 + 12x, where y is the height of the arch. The maximum       Log On


   

Question 253303: An arch is built so that it is 6 feet wide at the base. Its shape can be represented by a parabola with the equation y = -2x2 + 12x, where y is the height of the arch. The maximum height, y, of the arch is blank feet
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+-2x%5E2%2B12x
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+=+%28-b%29%2F2a where: a = -2 and b = 12, so...
x+=+%28-12%29%2F2%28-2%29
x+=+12%2F4
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%5E2%2B12x Substitute x = 3.
y+=+-2%283%29%5E2%2B12%283%29
y+=+-18%2B36
highlight%28y+=+18%29feet. This is the maximum height of the arch.