How do I use the vertex formula to determine the vertex of the graph for f(x)=3x^2-6x+1?

May 10, 2015

Vertex form: $y = a {\left(x + \frac{b}{2 a}\right)}^{2} + f \left(- \frac{b}{2} a\right)$.

-b/2a = 6/6 = 1

f(1) = 3 - 6 + 1 = -2

Vertex form $f \left(x\right) = 3 {\left(x - 1\right)}^{2} - 2.$

Check.
Develop: f(x) = 3(x^2 - 2x + 1) - 2 = 3x^2 - 6x + 3 - 2 =
f(x) = 3x^2 - 6x + 1. Correct.