Question

Find the vertex of the parabola whose equation is y=x² + 8x + 12. O(-4.12) 0 (4.4) O (0.-6) Find the vertex of the parabola whose equation is y = x² + 8x + 12 . O ( -4.12 ) 0 ( 4.4 ) O ( 0. - 6 )

Answer 1

Recall that the equation of a parabola in vertex-form is as follows:

`y=a(x-h)+k,`

where (h,k) is the vertex of the parabola, and a is a constant.

Notice that:

`\begin{gathered} x^2+8x+12=x^2+8x+12+4-4=x^2+8x+16-4 \\ =(x+4)^2-4. \end{gathered}`

Then:

`y=(x-(-4))^2-4.`

Therefore the vertex of the given parabola is (-4,-4).

Answer: (-4,-4).