Determine the quadratic function whose graph is given.
-The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x) = 2x² - 24x + 690, where x is the number of videos rented daily. Find the lowest cost to the nearest
Dollar.

Question

Quizplus · Accepted Answer

The lowest cost can be found by calculating the vertex of the quadratic equation, which represents the minimum point for a parabola that opens upwards. The vertex formula is given by $(-b/2a, C(-b/2a))$, where $a = 2$, $b = -24$, and $C(x)$ is the cost function. Plugging these values into the formula gives the x-coordinate of the vertex as $x = -(-24)/(2*2) = 6$. Substituting $x = 6$ into the cost function $C(x) = 2(6)^2 - 24(6) + 690$ gives the minimum cost, which rounds to $618.

Determine the Quadratic Function Whose Graph Is Given