Question

find the vertex.
$f(x) = 3x^2 - 12x + 4$
$(?, \square)$

Explanation:

Step1: Find x-coordinate of vertex

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

Step2: Find y-coordinate of vertex

Substitute $x=2$ into $f(x)$:
$f(2)=3(2)^2 -12(2)+4=3\times4 -24 +4=12-24+4=-8$

Answer:

$(2, -8)$