NSW Y11 Maths - Extension 1 Functions Inequalities -Quadratic

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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.

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 \(|ax+b| > k\)

Ref: https://educationstandards.nsw.edu.au/