SOLUTION: An arch is in the shape of a parabola. It has a span of 256 meters and a maximum height of 32 meters.
a. Find the equation of the parabola.
b. Determine the distance from the c
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Question 1204076: An arch is in the shape of a parabola. It has a span of 256 meters and a maximum height of 32 meters.
a. Find the equation of the parabola.
b. Determine the distance from the center at which the height is 12 meters.
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Let the origin be at the center of the base of the arch. The vertex is then (0,32) and the equation is of the form
Determine the coefficient a using the fact that the feet of the arch are at (-128,0) and (128,0).
ANSWER (a): The equation of the arch is
To find the distance from the center where the height is 12, set y=12 in the equation and solve for x.
That is 101.2 meters, to the nearest tenth.
ANSWER (b): approximately 101.2 meters
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Note the second question answered by tutor @MathLover1 is not the question that was asked....
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
a. Find the equation of the parabola.
a span of meters , coordinate of the vertex is meters and a maximum height of
Vertex at ( , )
vertex form of the equation is
, ( , ) is the vertex
the parabola starts at ( , ) that is a point ( , )
so, equation is
b. Determine the distance from the center at which the height is meters.
the height of the arch feet from the center
center is at , meters from the center so
approximately
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