Find an equation in standard form for the image of the graph of y=-.5x^2 under the translation of T(2,-4)
vertex form for a quadratic ...
$\displaystyle y = a(x - h)^2 + k$ , where $\displaystyle (h,k)$ are the vertex coordinates.
$\displaystyle y = -\frac{1}{2}(x - 0)^2 + 0$
moving the vertex of the parabola from $\displaystyle (0,0)$ to $\displaystyle (2,-4)$ ...
$\displaystyle y = -\frac{1}{2}(x-2)^2 - 4$