# Math

The rainbow bridge of Utah is a natural arch that is approximately parabolic in shape. The arch is about 88m high. It is 84m across the base. Determine a quadratic relation, in standard form, that models the shape of the arch

But the textbook said the answer is y=-22/441x^2+88/21x

I was wondering why is that the answer.

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1. Depends where you place the arch on your graph.
I centered mine so the top is (0,88) and its x-intercepts are (42, 0) and (-42,0)

so using the vertex form of the parabola equation, I get
y = ax^2 + 88
but (42,0) lies on it
0 = 1764a + 88
a = -88/1764 = -22/441

which yields the same answer as yours.

If we place one end at (0,0) and the other at (84,0)
the vertex is (42,88) and we get
y = a(x-42)^2 + 88
sub in (0,0)
0 = 1764a + 88
the same a = -22/441
so y = -22/441(x - 42)^2 + 88
which when expanded yields their answer
(I was hoping for that)

Poorly worded question, since they should have indicated where the vertex was to be placed.

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2. Would my answer be wrong if I used it on a test?

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3. no, it would be correct if you included a sketch.
I would give you full marks.

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