Question

Find the vertex of the parabola whose equation is y = x2 + 6x + 2.

Answer 1

the vertex would be (-3,-7)

Answer 2

Answer: The vertex of the given parabola is (-3, -7).

Step-by-step explanation: We are given to find the vertex of the parabola with the following equation :

`y=x^2+6x+2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the vertex form of a parabola is given by

`y=a(x-h)^2+k,` where (h, k) is the vertex of the parabola.

From equation (i), we have

`y=x^2+6x+2\\\\\Rightarrow y=(x^2+6x)+2\\\\\Rightarrow y=(x^2+2* x*3+3^2)+2-3^2\\\\\Rightarrow y=(x+3)^2+2-9\\\\\Rightarrow y=(x+3)^2-7\\\\\Rightarrow y=(x-(-3))^2+(-7).`

Comparing the above equation with the vertex form, we get

vertex, (h, k) = (-3, -7).

Thus, the vertex of the given parabola is (-3, -7).