SOLUTION: a bridge cable connecting two towers forms a parabola. the lowest point is 55m about the waters surface. the origin is at the point where the cable is attached to the southern towe

Question 1142336: a bridge cable connecting two towers forms a parabola. the lowest point is 55m about the waters surface. the origin is at the point where the cable is attached to the southern tower 75m above the waters surface. the other end is attached to the northern tower 120 m away, write a quadratic function in standard form
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a bridge cable connecting two towers forms a parabola. the lowest point is 55m about the waters surface. the origin is at the point where the cable is attached to the southern tower 75m above the waters surface. the other end is attached to the northern tower 120 m away, write a quadratic function in standard form
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No vertical info is given for the northern tower.
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Alan is right; since you don't say what height the cable attaches to the northern tower, the question as stated can't be solved.

So let's assume the logical thing -- that the cable is connected to both towers the same height above the water.

We are told to use as the origin the point where the cable attaches to the southern tower. So one point on the parabola is (0,0).

Since the two towers are 120m apart, another point on the parabola is (120,0).

By symmetry, the minimum point on the parabola is halfway between the two towers. Since the point where the cable attaches to each of the two towers is 75m above the water and the lowest point of the cable is 55m above the water, the minimum point on the parabola (the vertex) is (60,-20).

So a vertex form of the equation of the parabola is

To find the value of a, use one of the two other known points on the parabola.

In vertex form, the equation of the parabola is

You can convert that to whatever form you need.
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