Question 294733
The minimum is the C(x) value that is the smallest (ie it is the smallest cost value). This minimum occurs at the vertex (h,k) where 


{{{h=-b/2a}}}


In this case, {{{b=-16}}} and {{{a=4}}} meaning that {{{h=-(-16)/(2(4))=16/8=2}}}. In other words, if 2 thousand autos are produced, then the cost will be at a minimum. Simply plug this value into the function to get:


{{{C(2)=4(2)^2-16(2)+32=4(4)-16(2)+32=16-32+32=16}}} which means that {{{C(2)=16}}}. So the minimum cost is 16 million dollars (when 2 thousand autos are manufactured).



So the vertex is the point (2,16). What this means is that if we graph {{{C(x)= 4x^2-16x+32}}}, the lowest point on the graph is (2,16)