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Ihatemath123456789 Group Title

Although a football field appears to be flat, its surface is actually shaped like a parabola so that rain runs off either side. The cross section of a field with synthetic turf can be modeled by y=-0.000234(x-80)^2+1.5, where x and y are measured in feet. What is the fields width? What is the maximum height of the field's surface? (And I do not know what kind of problem this is because my Algebra2 teacher is ugly and doesn't want to tell his class what kind of problem it is_

  • one year ago
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  1. richyw Group Title
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    what do you mean "doesn't want to tell the class what kind of problem it is"?. It's a math problem.

    • one year ago
  2. Ihatemath123456789 Group Title
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    I'm pretty sure there are different way to solve it, but he didn't tell use which CORRECT way to solve it.

    • one year ago
  3. richyw Group Title
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    anyways if \(y=-0.000234(x-80)^2+1.5\) is your function, I would assume that this represents the height of the field, and that the edges of the field have a height of zero.

    • one year ago
  4. richyw Group Title
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    so you have your equation in vertex form. For a parabola in the form \[a(x-h)^2+k\] you have a vertex at the point \(h,k\). If \(a<0\) this will be the maximum point, if \(a>0\) the function will have no maximum.

    • one year ago
  5. richyw Group Title
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    So now you have the maximum height, and you just need to find the width. To find the width you just need to find where \(a(x-h)^2+k=0\). There are a bunch of ways to do this, but you should find two points. The distance between those two points will give you the width of the field. Make sense?

    • one year ago
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