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) $a = - \frac{1}{20}$ (c) $100 < x <1500$

2024 CGSS P1 Q2

2024 CGSS P1 Q2