Answer:
The focus is at;
[tex](-2,2)[/tex]
Explanation:
Given the parabola equation;
[tex](x+2)^2=4(y-1)[/tex]
Recall that the standard parabola equation can be written as;
[tex]\begin{gathered} (x-h)^2=4p(y-k) \\ \text{where the focus is at;} \\ f=(h,k+p) \end{gathered}[/tex]
For the given equation;
[tex]\begin{gathered} h=-2 \\ k=1 \\ p=1 \end{gathered}[/tex]
so, the focus would be;
[tex]\begin{gathered} f=(h,k+p) \\ f=(-2,1+1) \\ f=(-2,2) \end{gathered}[/tex]
Therefore, the focus is at;
[tex](-2,2)[/tex]
