g(x) is a parabola because of the x^2 and since it's "1·x^2," we know the parabola opens up.
This tells us it has a minimum at the vertex.
To find the x-coordinate of the vertex, we use [tex]x=\frac{-b}{2a}[/tex]:
[tex]x=\dfrac{-6}{2(1)} = -3[/tex]
To find the y-coordinate, we plug -3 in for x:
g(-3) = (-3)^2 + 6(-3) - 9
= 9 - 18 - 9
= -18
The vertex is the point (-3, -18).
The minimum value of this function is the y-value of the vertex: -18
(In general the minimum value of a function is the least y-value used anywhere on the function.)
