SOLUTION: An arch in the shape of a parabola has height 630ft and width 630ft. How wide is the arch 300 ft up?
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Question 1132760: An arch in the shape of a parabola has height 630ft and width 630ft. How wide is the arch 300 ft up?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
An arch in the shape of a parabola has height and width . How wide is the arch up?
The width of the bridge is feet so the parabola crosses the x-axis with x-coordinates ± = ±
=> x-intercepts are at (,) and (,)
Assume that it stands on the x axis, that it is symmetric with respect to the y-axis, and that it is feet wide at the base and feet high at the .
Then the maximum height occurs at ; so, the vertex of the parabola is =>(,)
Since the curve is a parabola which opens downward its equation can be written
since and
x-intercepts are at (,), use x-intercept to find
and, equation is
to find how wide is the arch up, substitute
= ±
the arch ft have intercepts at (,) and (,), so width will be the distance from to which is ft
answer: the arch ft up is ft wide
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