a company plans to sell bicycle helmets for $26 each. the companys business manager estimates that the cost…

a company plans to sell bicycle helmets for $26 each. the companys business manager estimates that the cost, y, of making x helmets is a quadratic function with a y - intercept of 8,400 and a vertex of (500, 15,900).\nx = number of helmets\ny = amount in dollars\nwhich system models this situation?\no y = 26x and y = 8,400(x - 500)^2+15,900\no y = 26x and y = -0.030(x - 500)^2+15,900\no y = x/26 and y = -0.030(x - 500)^2+15,900\no y = x/26 and y = 8,400(x - 500)^2+15,900

a company plans to sell bicycle helmets for $26 each. the companys business manager estimates that the cost, y, of making x helmets is a quadratic function with a y - intercept of 8,400 and a vertex of (500, 15,900).\nx = number of helmets\ny = amount in dollars\nwhich system models this situation?\no y = 26x and y = 8,400(x - 500)^2+15,900\no y = 26x and y = -0.030(x - 500)^2+15,900\no y = x/26 and y = -0.030(x - 500)^2+15,900\no y = x/26 and y = 8,400(x - 500)^2+15,900

Answer

Explanation:

Step1: Find the revenue - function

The company sells each helmet for $26. If $x$ is the number of helmets, the revenue $y$ (amount of money made from selling helmets) is given by the linear function $y = 26x$.

Step2: Find the cost - function

The vertex - form of a quadratic function is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex of the parabola. Here, the vertex is $(h,k)=(500,15900)$, so the cost function is $y=a(x - 500)^2+15900$. The $y$ - intercept is 8400, which means when $x = 0$, $y=8400$. Substitute $x = 0$ and $y = 8400$ into $y=a(x - 500)^2+15900$: [ \begin{align*} 8400&=a(0 - 500)^2+15900\ 8400&=a\times250000+15900\ a\times250000&=8400 - 15900\ a\times250000&=- 7500\ a&=\frac{-7500}{250000}=-0.03 \end{align*} ] So the cost function is $y=-0.03(x - 500)^2+15900$.

Answer:

B. $y = 26x$ and $y=-0.030(x - 500)^2+15900$