Solve the problem.
-The owner of a video store has determined that the cost $C$, in dollars, of operating the store is approximately given by $C ( x ) = 2 x ^ { 2 } - 26 x + 640$, where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.
A) $\$ 556$
B) $\$ 302$
C) $\$ 471$
D) $\$ 725$

Question

Quizplus · Accepted Answer

The lowest cost can be found by determining the vertex of the parabola represented by the given quadratic equation $C(x) = 2x^2 - 26x + 640$. The x-coordinate of the vertex is given by $-\frac{b}{2a}$, where $a = 2$ and $b = -26$. Calculating this gives $x = \frac{26}{4} = 6.5$. Substituting $x = 6.5$ back into the equation gives the minimum cost, $C(6.5) = 2(6.5)^2 - 26(6.5) + 640 = 2(42.25) - 169 + 640 = 84.5 - 169 + 640 = 555.5$, which rounds to $\$556$.

Solve the Problem CCC , in Dollars, of Operating the Store Is Approximately Given

Solve the Problem $C$ , in Dollars, of Operating the Store Is Approximately Given