Discriminants (AQA A-Level Mathematics): Flashcards

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Discriminants
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Symbol for the discriminant

Δ\Delta (Delta)

Formula for discriminant Δ\Delta

b24acb^2 - 4ac

Nature of roots when Δ>0\Delta > 0

Two distinct real roots

Nature of roots when Δ=0\Delta = 0

One real root (repeated)

Nature of roots when Δ<0\Delta < 0

No real roots (complex)

Direction of parabola when a>0a > 0

Opens upwards

Direction of parabola when a<0a < 0

Opens downwards

Vertex x-coordinate for y=ax2+bx+cy = ax^2 + bx + c

x=b2ax = -\frac{b}{2a}

Y-intercept of y=ax2+bx+cy = ax^2 + bx + c

cc

Condition for two distinct real roots

Δ>0\Delta > 0

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