Question 979420
Standard Form of Parabola Equation:  {{{y=a(x-h)^2+k}}}.


Clearance of 40 feet above means that (h,k) is (0,40), if you want the maximum point
to be directly over the origin, or symmetry axis at x=0.  This makes for equation
{{{y=a(x-0)^2+40}}}  or {{{y=ax^2+40}}}.


Span of 160 feet, if this is from one end of the arch horizontally to the other end of the arch,
means that the roots of the equation would be at  {{{-160/2}}} and  {{{160/2}}}; or -80 and 80.
Either of these will be used to solve for coefficient, a.
-
{{{y-40=ax^2}}}
{{{a=(y-40)/x^2}}}
{{{a=(0-40)/(80)^2}}}
{{{a=-40/6400=-4/640=-1/160}}}


Resulting equation, {{{highlight(y=-(1/160)x^2+40)}}}