Question

Please solve this, also, pls ignore the part that's scratched/ crossed out :)

Answer 1

`-2x+y^2-2y+5=0`

The standard form is given by:

`\begin{gathered} y=Ax^2+Bx+C \\ or \\ x=Ay^2+By+C \end{gathered}`

Therefore:

`x=(y^2)/(2)-y+(5)/(2)`

The vertex is the point V(h,k) which is given by:

`\begin{gathered} k=(-b)/(2a) \\ h=y(k) \\ ---- \\ k=-(-1)/(2((1)/(2)))=1 \end{gathered}`
`y(1)=(1^2)/(2)+-1+(5)/(2)=2=h`

Therefore, the vertex is:

`V=(2,1)`

the focus is:

`(3,1)`

And the directrix is:

`x=1`