Question 420990
In skeet shooting, the clay pigeon is launched from a height of 4 feet and reaches a maximum height of 164 feet at a distance of 80 feet from the launch site.
a) write an equation for the height of the clay pigeon in terms of the horizontal distance it has traveled?

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Standard form for a parabola:

y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
From given data, h=80 and k=164.
The problem, then, is to find A.
y=A(x-80)^2+164
at x=0, y=4 (lauching height)
4=A(0-80)^2+164
-160=A(-80)^2=6400
A=-160/6400=-1/40
Equation:
y=-(1/40)(x-80)^2+164
See the graph of this equation below:

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{{{ graph( 300, 300, -20, 200, -200, 200, -(1/40)(x-80)^2+164) }}}