Question

What is the vertex form of f(x) = x2 + 6x + 3

Answer 1

Answer:
`y=(x +3)^2 -6`

Explanation:

The equation of a parabola in Vertex form is:

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

Where
`(h,k)` is the vertex of the parabola

We can rewrite the function
`f(x)= x^2 + 6x + 3` as:

`y= x^2 + 6x + 3`

In order to convert it into vertex form we need to Complete the square:

Take the coefficient of the x term, divide it by 2 and square it:

`((6)/(2))=3^2`

Add and subtract 3² on the right side:

`y= x^2 + 6x+3^2 + 3-3^2`

Now we must convert the right side to a squared expression, then we get:

`y=(x +3)^2 -6`