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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_

Mathematics
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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.
I'm pretty sure there are different way to solve it, but he didn't tell use which CORRECT way to solve it.
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.

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Other answers:

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.
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?

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