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=(1)/(2) \end{gathered}`
`\text{Directrix : y=}(3)/(2)`
`\text{Focus: (-2,}(1)/(2))`
`\text{Vertex: (-2,1)}`