Question 703933
The only way that both the x-intercept and
the axis of symmetry can {{{ - 6 }}} is if the 
parabola just touches the x-axis and thus
only has 1 solution- called a double root.
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If the y intercept is positive, that tells me 
the parabola has a minimum and not a maximum.
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If the form is:
{{{ y = a*x^2 + b*x + c }}}
The roots ( x-intercepts ) are given by:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
When there is a double root, 
{{{ b^2 = 4*a*c }}}
{{{ a = b^2/(4c) }}}
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The y-intercept occurs at ( 0,36 ), so
{{{ 36 = a*0 + b*0 + c }}}
{{{ c = 36 }}}
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The x-coordinate of the axis of symmetry is at {{{ -b/(2a) }}}
{{{ -6 = -b/(2a) }}}
{{{ b = 12a }}}
By substitution:
{{{ b = 12*( b^2 / ( 4*36) ) }}}
{{{ 144b = 12b^2 }}}
{{{ b = 12 }}}
and, since
{{{ b = 12a }}}
{{{ a = b/12 }}}
{{{ a = 12/12 }}}
{{{ a = 1 }}}
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The equation is
{{{ y = x^2 + 12x + 36 }}}
{{{ y = ( x + 6 )^2 }}}
Here's the plot:
{{{ graph( 400, 400, -14, 2, -2, 50, ( x + 6 )^2 ) }}}