Question

what are the coordinates of the vertex of the function $f(x) = x^2 - 12x + 5$?
(6, 31)
(-6, 31)
(6, -31)
(-6, -31)

Explanation:

Step1: Find x-coordinate of vertex

For $f(x)=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=1$, $b=-12$, so:
$x=-\frac{-12}{2(1)}=6$

Step2: Find y-coordinate of vertex

Substitute $x=6$ into $f(x)$:
$f(6)=(6)^2 -12(6)+5=36-72+5=-31$

Answer:

(6, -31)