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

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) (Show Source): You can put this solution on YOUR website!

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:
where: a = -2 and b = 12, so...

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.
Substitute x = 3.

feet. This is the maximum height of the arch.
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