Question

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

Answer 1

Answer:

$(1,-3)$

Step-by-step 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 $(1,-3)$.