Question 426564: The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x)=2x^2-32x+540, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar." Answer by ewatrrr(10682) (Show Source):
Using the vertex form of a parabola, where(h,k) is the vertex
C(x)=2x^2-32x+540 |Completing the square to find the vertex (parabola opens upward)
C(x)=2[(x-8)^2 - 64] +540
C(x)=2(x-8)^2 -128 +540
C(x)=2(x-8)^2 +412 |(8,412) the vertex point. $412 the lowest cost.