Resources for Inequalities -Quadratic
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Questions
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Video Tutorials
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Inequalities -Quadratic Theory
NSW Y11 Maths - Extension 1 Functions Inequalities -Quadratic
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Inequalities -Quadratic - Video - Quadratic Inequalities
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Theory
A quadratic inequality can be in two forms:
- The factored form \(\left( {x - a} \right)\left( {x - b} \right) > 0\)
- The unfactored form \(a{x^2} + bx + c \le 0\)
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.
Syllabus Reference
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 \(|ax+b| > k\)