SOLUTION: Find a function p(x) for an arch that is 15 feet tall and 16 feet wide at the base

Question 1097745: Find a function p(x) for an arch that is 15 feet tall and 16 feet wide at the base
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The arch is in the shape of a parabola. Let us choose the coordinates so that the vertex is at (0,15)
Then the equation will take on the form p(x) = y = ax^2 + c
Since the base is 16 feet wide, the parabola intersects the y-axis at the points (8,0) and (-8,0)
When x = 0, the constant term c = 15
Use one of the other points to find a:
0 = a*8^2 + 15
a = -15/64
Thus one function which describes the arch is p(x) = (-15/64)x^2 + 15
Note that the coefficient a is equal to -h/(b/2)^2, where h = the height and b = the base
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