Answer
$(y-3)^{2}=-12(x-4)$
New focus: $\quad (1, 3)$
New directrix: $\quad x=7$
New vertex:$ \quad (4,3)$
Work Step by Step
Shift right by 4 $\Rightarrow$ in the equation, replace $x$ with $x-4$
Shift up by 3 $\Rightarrow$ in the equation, replace $y$ with $y-3$
New equation:$\quad (y-3)^{2}=-12(x-4)$
$y^{2}=-12x\quad $is of the form
$y^{2}=-4px $ ,$\qquad x=\displaystyle \frac{y^{2}}{4p}$ ,$\qquad$ (opens left), $p=3$
focus: $\quad(-p,0)$= $\quad(-3,0)$
directrix: $ x=p\Rightarrow \quad x=3$
vertex:$\quad (0,0)$
The translations are such that $(x,y)\rightarrow(x',y')$, where
$\left\{\begin{array}{ll}
x'=x+4 & \text{... shift rightt}\\
y'=y+3 & \text{... shift up}
\end{array}\right.$
New focus: $\quad(-3+4,0+3) = (1, 3)$
New directrix: $ x=3+4\Rightarrow \quad x=7$
New vertex:$\quad (0+4,0+4) = (4,3)$
