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Quadratic models in real-world contexts

Quadratic models in real-world contexts

Secondary 2

A shop sells cups at \(\$x\) each. Its daily profit, \(\$P\), is modelled by \(P=-2x^2+28x-80\).

  1. Find the daily profit when each cup is sold at \(\$5\).
  2. Find the two selling prices at which the shop makes no profit.
  3. Use your answer to (b) to find the selling price that gives the greatest profit, and state that profit.

Solution:

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Answer:(a) \(\$10\) (b) \(\$4\) or \(\$10\) (c) \(\$7\), profit \(\$18\)

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