Question

what is the vertex of $g(x) = 3x^2 - 12x + 7$?
$\bigcirc$ $(-6, -5)$
$\bigcirc$ $(-2, -5)$
$\bigcirc$ $(2, -5)$
$\bigcirc$ $(6, -5)$

Explanation:

Step1: Find x-coordinate of vertex

For $g(x)=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=3$, $b=-12$, so:
$x=-\frac{-12}{2\times3}=\frac{12}{6}=2$

Step2: Find y-coordinate of vertex

Substitute $x=2$ into $g(x)$:
$g(2)=3(2)^2-12(2)+7=3\times4-24+7=12-24+7=-5$

Answer:

(2, -5)