Question

What are the coordinates of the vertex for f(x)= x^2 +6x +13

Answer 1

(-3,4)

Explanation:

So we have the quadratic function:

`f(x)=x^2+6x+13`

The formula for the x-coordinate of the vertex is:

`x=-b/2a`

From the function, we can determine that a is 1, b is 6, and c is 13. Thus:

`x=-(6)/2(1)`

Multiply:

`x=-6/2`

Divide:

`x=-3`

Now, substitute this back into the function to solve for the y-coordinate:

`f(-3)=(-3)^2+6(-3)+13`

Square and multiply:

`f(-3)=9-18+13`

Add:

`f(-3)=4`

So, the vertex is (-3,4)

And we're done!