Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Secondary 3

The function \[\mathrm{f}(x)=-(x-2)^2+9\] is defined only for \(0\leq x\leq5.\)

  1. Find its maximum and minimum values, stating where each occurs.

  2. State its range.

  3. A student says, “A downward-opening quadratic has no minimum.” Explain why that statement is incorrect here.

Solution:

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Answer:(a) Maximum \(9\) at \(x=2\); Minimum \(0\) at \(x=5\); (b) Range \(0\leq \mathrm{f}(x)\leq9\).

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