Question

In the parabola y = (x + 12 + 2, what is the vertex?

Answer 1

The vertex is the point (-6,-34)

Explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

`y=a(x-h)^(2)+k`

where

(h,k) is the vertex of the parabola

In this problem we have

`y=x^(2)+12x+2`

Convert in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`y-2=x^(2)+12x`

Complete the square . Remember to balance the equation by adding the same constants to each side.

`y-2+36=x^(2)+12x+36`

`y+34=x^(2)+12x+36`

Rewrite as perfect squares

`y+34=(x+6)^(2)`

`y=(x+6)^(2)-34`

The vertex is the point (-6,-34)