The Solution:
The formula for the equation of the parabola is
[tex]x=a(y-k)^2+h[/tex]In this case,
[tex]\begin{gathered} k=1 \\ h=-3 \\ x=-4 \\ y=-1 \end{gathered}[/tex]Substituting these values,
[tex]\begin{gathered} -4=a(-1-1)^2-3 \\ -4=a(-2)^2-3 \end{gathered}[/tex][tex]\begin{gathered} -4=4a-3 \\ -4+3=4a \\ -1=4a \end{gathered}[/tex]Dividing both sides by 4, we get
[tex]a=-\frac{1}{4}[/tex]Thus, the equation of the parabola is:
[tex]\begin{gathered} x=-\frac{1}{4}(y-1)^2-3 \\ \text{ }x+3=-\frac{1}{4}(y-1)^2 \end{gathered}[/tex][tex]\begin{gathered} a=-\frac{1}{4} \\ \\ h=-3 \\ \\ k=1 \end{gathered}[/tex]