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

Explanation:

Step1: Identify coefficients

For the quadratic function $g(x)=3x^{2}-12x + 7$, $a = 3$, $b=-12$, $c = 7$.

Step2: Find x - coordinate of vertex

Use the formula $x=-\frac{b}{2a}$. Substitute $a = 3$ and $b=-12$ into it: $x=-\frac{-12}{2\times3}=\frac{12}{6}=2$.

Step3: Find y - coordinate of vertex

Substitute $x = 2$ into the function $g(x)=3x^{2}-12x + 7$. Then $g(2)=3\times2^{2}-12\times2 + 7=3\times4-24 + 7=12-24 + 7=-5$.

Answer:

C. $(2,-5)$