Question 47648
start with {{{y = x^2}}}
{{{ graph( 200, 300, -5, 5, -4, 20, x^2) }}}
Shift 4 units to the right
{{{y = (x-4)^2}}}
{{{ graph( 200, 300, -2, 10, -4, 20, (x-4)^2) }}}
Stretch in the vertical direction by factor of 5
{{{y = 5*(x-4)^2}}}
{{{ graph( 200, 300, -2, 10, -4, 20, 5*(x-4)^2) }}}
Reflect about the x-axis
{{{y = -5*(x-4)^2}}}
{{{ graph( 200, 300, -2, 10, -20, 4, -5*(x-4)^2) }}}
Shift 8 units upward
{{{y - 8 = -5*(x-4)^2}}}
{{{ graph( 200, 300, -2, 10, -10, 20, 8-5*(x-4)^2) }}}
Solving for y,
{{{y - 8 = -5*(x^2 -8x + 16)}}}
{{{y = -5*(x^2 -8x +16) + 8}}}
{{{y = -5*x^2 + 40x - 80 + 8}}}
{{{y = -5*x^2 + 40x -72}}}
Check some values to see if they make sense
When x = 4,
{{{y = -80 + 160 -72}}}
{{{y = + 8}}}
OK
Find roots (solve for y=0) use  {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
where {{{a*x^2 + b*x + c = 0}}}
a = -5
b = 40
c = -72
{{{x = (-40 +- sqrt( 40^2-4*(-5)*(-72) ))/(2*(-5)) }}}
{{{x = (-40 +- sqrt(1600 - 1440)) / -10}}}
{{{x = 4 +- sqrt(160) / -10}}}
{{{x = 4 +- 4*sqrt(10) / 10}}}
{{{x = 4 + 1.265}}}
{{{x = 4 - 1.265}}}
These values make sense according to graph