Question

Complete the square

to find the vertex
of this parabola.
y^2+6y+8x+1=0
([?], [?])

Answer 1

`(1,-3)`

Explanation:

Complete the squares

`y^2+6y+8x+1=0\\\\y^2+6y=-8x-1\\\\y^2+6y+9=-8x-1+9\\\\(y+3)^2=-8x+8\\\\(y+3)^2=-8(x-1)`

We now compare to the equation
`(y-k)^2=2p(x-h)` where
`(h,k)` is the vertex of the parabola. Hence, the vertex of the parabola is
`(1,-3)`.