The profit, $\$y$ of a company can be modelled by the equation $y = a(x - h)^2 + k$, where

Question

The profit, $\$y$ of a company can be modelled by the equation $y = a(x - h)^2 + k$, where $x$ is the number of goods sold and $a$, $h$ and $k$ are constants. The company obtained the maximum profit of $\$24\,500$ when $800$ goods were sold. The company incurred a loss of $\$7\,500$ when no goods were sold. State the value of $h$ and of $k$.[2] Using the values of $h$ and $k$ found in part (a), find the value of $a$. [2] Find the range of the number of goods the company needed to sell to earn a profit.[2]

Accepted Answer

(a) $h=800$, $k=24\,500$ (b) $a=-\frac1{20}$ (c) $100<x<1500$, equivalently $101\le x\le1499$ whole goods

2024 CGSS P1 Q2

2024 CGSS P1 Q2

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