Question

Can you please help me with 42Graph the parabola, labeling the focus and the directrix

Answer 1

Given:

$x^2+4x+2y+2=0$$\begin{gathered} x^2+4x+4-4+2y+2=0 \\ x^2+4x+4+2y-2=0 \\ x^2+4x+4=2-2y \\ (x+2)^2=-2(y-1) \\ X^2=-2Y \end{gathered}$

Compare with,

$x^2=-4ay$$\begin{gathered} 4a=2 \\ a=\frac{1}{2} \end{gathered}$$\text{Directrix : y=}\frac{3}{2}$$\text{Focus: (-2,}\frac{1}{2})$$\text{Vertex: (-2,1)}$