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

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)