Question 750248
Think of this as a parabola that opens downward, and
the base, or the road, is the x-axis. The y-axis goes 
through the maximum height. The x-intercepts are at
(  9,0 ) and ( -9,0 ), making the base 18 wide
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The vertex of the parabola is at ( 0,10 )
Find the equation of the parabola
It will have the general form
{{{ y = a*x^2 + b*x + c }}}
The x-coordinate of the vertex is at
{{{ x[v] = -b/(2a) }}} I have stated that  {{{ x[v] = 0 }}}
{{{ 0 = -b/(2a) }}}
{{{ b = 0 }}}
So far, I have
{{{ y = a*x^2 + 0*x + c }}}
{{{ y = a*x^2 + c }}}
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Also, the vertex is at ( 0,10 ), so I can say
{{{ 10 = a*0 + c }}}
{{{ c = 10 }}}, and so far I have
{{{ y = a*x^2 + 10 }}}
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The other points I have are ( -9,0 ) and ( 9,0 )
If I say {{{ y = 0 }}}
{{{ ax^2 + 10 = 0 }}}
If {{{ x = -9 }}} or {{{ x = 9 }}}, then
{{{ a*81 + 10 = 0 }}}
{{{ 81a = -10 }}}
{{{ a = -10/81 }}}
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The whole equation is:
{{{ y = (-10/81)*x^2 + 10 }}}
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Here's the plot:
{{{ graph( 400, 400, -12, 12, -2, 12, (-10/81)*x^2 + 10 ) }}} 
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What they want to know is:
What is {{{x}}} when {{{ y = 7.5 }}}, and
What is {{{-x}}} when {{{ y = 7.5 }}}
Then you find {{{ 2x }}}, which is the width of the truck.
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{{{ y = (-10/81)*x^2 + 10 }}}
{{{ 7.5 = (-10/81)*x^2 + 10 }}}
{{{ (-10/81)*x^2 = -2.5 }}}
{{{ x^2 = ( 2.5*81) / 10 }}}
{{{ x^2 = 20.25 }}}
{{{ x = 4.5 }}}
{{{ 2x = 9 }}}
The maximum width of the truck is 9 m
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check:
{{{ y = (-10/81)*x^2 + 10 }}}
{{{ y = (-10/81)*4.5^2 + 10 }}}
{{{ y = (-10/81)*20.25 + 10 }}}
{{{ y = -202.5/81 + 810/81 }}}
{{{ y = ( 810 - 202.5 ) / 81 }}}
{{{ y = 607.5/81 }}}
{{{ y = 7.5 }}}
OK