Quadratic Inequalities (HSC SSCE Mathematics Advanced): Flashcards

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Quadratic Inequalities
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Quadratic inequality definition

Compares quadratic function to constant/function via inequality symbol

General form of quadratic function

f(x)=ax2+bx+cf(x) = ax^2 + bx + c where a≠0a \neq 0

What are boundary points?

Points where parabola crosses the line

Formula for discriminant

Δ=b2−4ac\Delta = b^2 - 4ac

Meaning of Δ>0\Delta > 0

Two distinct boundary points

Meaning of Δ=0\Delta = 0

One boundary point

Meaning of Δ<0\Delta < 0

No boundary points

For f(x)>kf(x) > k, where is parabola?

Above the line y=ky = k

When to include boundary points

When inequality uses ≤\leq or ≥\geq

Form of quadratic inequality solution

Range(s) of values, not discrete points

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