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

My answer was y=-22/441x^2+88
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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