Question

learning target 2: i can represent mathematical situations as well as real - world situation: involving quadratic functions. 14. a company sells chapati. the amount of profit, y, made by the company by selling x by the function $y = -x^{2}+90x - 454$ based on this function. a) what is the maximum profit the company can make? round to the nearest dollar. (2 pts) b) how many chapati would need to be sold to make that maximum profit? (1 pt)

Explanation:

Step1: Find x for max profit

For quadratic $y=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=-1$, $b=90$:
$x = -\frac{90}{2(-1)} = 45$

Step2: Calculate max profit

Substitute $x=45$ into $y=-x^2+90x-454$:
$y = -(45)^2 + 90(45) - 454 = -2025 + 4050 - 454$

Answer:

a) 1571
b) 45