Question

Write each function in vertex form and identify its vertex. F(x)=x^2+6x+2

Answer 1

`y+7=(x+3)^2`

vertex (-3,-7)

Step-by-step explanation

`f(x)=x^2+6x+2`

Step 1

prepare to complete the square

`\begin{gathered} y=x^2+6x+2 \\ y+?\text{ = (}x^2+6x+\text{ ?) }+2 \\ \\ \end{gathered}`

Step 2

add 9 in both sides

`\begin{gathered} y+9=\mleft(x^2+6x+9\mright)+2 \\ y+9=(x+3)^2+2 \end{gathered}`

Step 3

write in vertex form

`\begin{gathered} y+9=(x+3)^2+2 \\ y+9-2=(x+3)^2 \\ y+7=(x+3)^2 \\ \\ \end{gathered}`

Step 4

the vertex is

(-3.-7)

I hope this helps you