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

User Lavrton
by
7.1k points

1 Answer

6 votes

Answer:

(-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!

User Jim Redmond
by
7.6k points