[tex]f(x) = 6x - 4 + x^2[/tex]
We complete the square to get vertex form.
[tex]f(x) = x^2 + 6x - 4[/tex]
[tex]f(x) = x^2 +6x + 9-9- 4[/tex]
[tex]f(x) = (x+3)^2-13[/tex]
The vertex form of the function is f(x) = (x – 2)2 + 2.
Nope.
The vertex of the function is (–3, –13).
Yes, that's easily seen from the vertex form we got.
The axis of symmetry for the function is x = 3.
Nope, x = -3 is the symmetry axis.
The graph increases over the interval (–3, infinity).
That's true; the minimum is at the vertex when the squared term is zero and it increases both ways from there.
The function does not cross the x-axis.
No, it does cross; its minimum is -13 and it goes up from there.
