Question 982017
Let the equation of the arch be:
{{{ h(x) = a*x^2 + b*x + c }}}
where {{{ h(x) }}} is the vertical location
of any point ( x,h ) on the arch.
and {{{ x }}} is the horizontal location 
of any point ( x,h ) on the arch
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The formula for the x-coordinate of the
vertex is:
{{{ x[v] = -b/(2a) }}}
Since the vertex is at the origin,
{{{ -b/(2a) = 0 }}}
{{{ b = 0 }}}
So, now the equation is:
{{{ h(x) = a*x^2 + c }}}
Plugging in the point ( 0-,0 ), I get
{{{ 0 = a*0 + c }}}
so, {{{ c = 0 }}}
Now the equation is:
{{{ h(x) = a*x^2 }}}
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I am given the points: 
( 14, -22 ) and
( -14, -22 )
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{{{ -22 = a*14^2 }}}
{{{ -22 = 196a }}}
{{{ a = -11/98 }}}
and
{{{ -22 = a*(-14)^2 }}}
{{{ -22 = 196a }}}
{{{ a = -11/98 }}}
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The equation is:
{{{ h(x) = -(11/98)*x^2 }}}
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check:
does it go through ( 14, -22 ) and ( -14, -22 ) ?
{{{ -22 = -(11/98)*14^2 }}}
{{{ -22 = -(11/98)*196 }}}
{{{ -22 = -22 }}}
You can check the other point ( -14, -22 )
Here's the plot:
{{{ graph( 400, 400, -20, 20, -26, 2, -(11/98)*x^2 ) }}}