A parabolic archway has the dimensions shown in Figure 15.42.

If we draw coordinate axes as shown, it can be shown that the equation of the archway portion is \[x^{2}=-4 c(y+3)\]
for some constant \(c\). Find the standard-form equation of the parabolic portion.

Figure 15.42

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3 ft y 12 ft 3 ft 13m oft 18 ft