Question

A furniture company wants to minimize its costs and has determined that when x
wooden chairs are built, the average cost per chair is given by
C(x)=0.01x2 -7x+1265

Answer 1

A quadratic equation like $ax^2+bx+c$ has a minimum if $a>0$ and a maximum if $a<0$ as critical points.

In both cases, the critical point has $x$ coordinate $-\frac{b}{2a}$

In your case, we have $a=0.01>0$, so the parabola has indeed a minimum, located at

$x=-\dfrac{-7}{0.01}=700$