Question 703939
The given parabola, {{{ y = (1/2)*x^2 }}}, opens upward ( has a minimum ),
and it's vertex is at the origin, (0,0)
Now you just have to translate the vertex to ( 4,-4 )
{{{ y - (- 4) = (1/2)*( x - 4 )^2 }}}
{{{ y + 4 = (1/2)*( x^2 - 8x + 16 ) }}}
{{{ 2y + 8 = x^2 - 8x + 16 }}}
{{{ 2y = x^2 - 8x + 8 }}}
{{{ y = (1/2)*x^2 - 4x + 4 }}}
Here are plots of both equations:
{{{ graph( 400, 400, -10, 10, -10, 10, (1/2)*x^2, (1/2)*x^2 - 4x + 4 ) }}}