NSW Y11 Maths - Extension 1 Functions Inequalities -Quadratic

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A quadratic inequality can be in two forms:

To solve an unfactored quadratic inequality the inequality is factorised and the ‘critical points’ or zeros are determined.

A number line is then used to determine where the values of \(x\) are valid for a specific inequality.

NSW Syllabus Reference: ME-F1.2 Inequalities. This will require student to

solve quadratic inequalities using both algebraic and graphical techniques
solve inequalities involving rational expressions, including those with the unknown in the denominator
solve absolute value inequalities of the form \(|ax+b| \ge k,\, |ax+b| \le k,\, |ax+b| <k\) and \(|ax+b| > k\)