Question

(x+3)^2=12(y+2)
identify the vertex, focus, axis of symmetry,and directrix

Answer 1

\[\text{ The vertex of } \\ (x-h)^2=4p(y-k) \\ \text{ is } (h,k) \\ \text{ We also know the parabola is a vertical parabola since the square part} \\ \text{ is on the x } \\ \text{ we know the directrix will be horizontal} \\ \text{ Also we know from this that the vertex and focus will share the same} \\ \text{ x-coordinate } \\ \\ \text{ so anyways we know the focus is therefore } (h,k+p) \\ \text{ and the directrix is } y=k-p \\ \text{ I will also provide a drawing }
\]