A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?
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Ok, it's a parabola so it has to fit the equation Y = squeeze factor * X^2 + yshift.
The yshift is 25 feet.
The squeeze factor will be negative for it to be an arch instead of a typical parabola.
At Y = zero the arch is spanning -20 to the left and 20 to the right.
So 0 = squeezefactor * 20^2 + 25
squeezefactor x 400 = -25
squeezefactor = - 1/16
Thus the equation for your parabola is Y = -1/16 * X^2 + 25.
Put 8 into the equation and Y = -(1/16) * 64 + 25 = -4 + 25 = 21 feet.
The yshift is 25 feet.
The squeeze factor will be negative for it to be an arch instead of a typical parabola.
At Y = zero the arch is spanning -20 to the left and 20 to the right.
So 0 = squeezefactor * 20^2 + 25
squeezefactor x 400 = -25
squeezefactor = - 1/16
Thus the equation for your parabola is Y = -1/16 * X^2 + 25.
Put 8 into the equation and Y = -(1/16) * 64 + 25 = -4 + 25 = 21 feet.