what are the coordinates of the vertex of the function f(x) = x² - 12x + 5?\n(6, 31)\n(-6, 31)\n(6…

Answer:

C. $(6, - 31)$

Explanation:

Step1: Recall vertex - x formula

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex is $x=-\frac{b}{2a}$. In $f(x)=x^{2}-12x + 5$, $a = 1$, $b=-12$, $c = 5$. Then $x=-\frac{-12}{2\times1}=6$.

Step2: Find y - coordinate

Substitute $x = 6$ into the function $f(x)=x^{2}-12x + 5$. So $f(6)=6^{2}-12\times6 + 5=36-72 + 5=-31$. So the vertex coordinates are $(6,-31)$.