Answer:
(-3,4)
Step-by-step explanation:
So we have the quadratic function:
[tex]f(x)=x^2+6x+13[/tex]
The formula for the x-coordinate of the vertex is:
[tex]x=-b/2a[/tex]
From the function, we can determine that a is 1, b is 6, and c is 13. Thus:
[tex]x=-(6)/2(1)[/tex]
Multiply:
[tex]x=-6/2[/tex]
Divide:
[tex]x=-3[/tex]
Now, substitute this back into the function to solve for the y-coordinate:
[tex]f(-3)=(-3)^2+6(-3)+13[/tex]
Square and multiply:
[tex]f(-3)=9-18+13[/tex]
Add:
[tex]f(-3)=4[/tex]
So, the vertex is (-3,4)
And we're done!
