Question 1029552
The general form is:
{{{ f(x) = a*x^2 + b*x + c }}}
The given equation is:
{{{ h(x) = -.00121246*x^2 + 876 }}}
{{{ a = -.00121246 }}}
{{{ b = 0 }}}
{{{ c = 876 }}}
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(a)
The formula for the x-value of the vertex is:
{{{ x[v] = -b/(2a) }}}
{{{ x[v] = 0 }}}
If you plug this back into the given equation, 
you get 
{{{ h(0) = -.00121246*0^2 + 876 }}}
{{{ h(0) = 876 }}}, the height at the top of the arch
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(b)
Given: {{{ h(x) = 525 }}}
{{{ h(x) = -.00121246*x^2 + 876 }}}
{{{ 525 = -.00121246*x^2 + 876 }}}
{{{ .00121246*x^2 = 876 - 525 }}}
{{{ .00121246*x^2 =351 }}}
{{{ x^2 = 289494.0864 }}}
{{{ x = 538.05 }}}
and
{{{ x = -538.05 }}}
The span of the arch at {{{ h(x) = 525 }}} is
{{{ 2*538 = 1076 }}}
1,076 ft span
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Here's the plot of the arch:
{{{ graph( 800, 400, -1000, 1000, -100, 1000, -.00121246*x^2 + 876 ) }}}