Quadratic Inequalities (Edexcel A-Level Mathematics): Flashcards

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Quadratic Inequalities
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What are quadratic inequalities?

Inequalities involving a quadratic expression (term with x2x^2)

Goal of solving quadratic inequalities

Find range of values for xx that makes inequality true

First step to solve quadratic inequality

Write in standard form with one side equal to 0

Second step: solve quadratic inequality

Find roots of ax2+bx+c=0ax^2 + bx + c = 0

Purpose of roots in quadratic inequalities

Divide number line into intervals

Graph circles for >> or << inequalities

Open circles

Graph circles for geqgeq or leqleq inequalities

Closed circles

When to use quadratic formula

When quadratic doesn't factorize easily

Parabola direction if x2x^2 coefficient is positive

Opens upward

Parabola direction if x2x^2 coefficient is negative

Opens downward

For <0< 0 or leq0leq 0, which regions to use?

Negative regions

For >0> 0 or geq0geq 0, which regions to use?

Positive regions

Calculator mode for quadratic inequalities

Inequality solving mode, degree 2, input coefficients

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