Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Secondary 3

Complete the square and state the maximum value and where it occurs.

  1. \( y=-x^2+6x-2. \)

  2. \( y=-2x^2-8x+1. \)

  3. \( y=12+4x-x^2. \)

Also state the range of \(y\).

Solution:

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Answer:(a) \(-(x-3)^2+7\); Maximum \(7\) at \(x=3\). (b) \(-2(x+2)^2+9\); Maximum \(9\) at \(x=-2\). (c) \(-(x-2)^2+16\); Maximum \(16\) at \(x=2\); range \(y\leq16\).

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