Sketching Polynomials (AQA A-Level Mathematics): Flashcards

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Sketching Polynomials
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Turning points in degree 1 polynomial

No turning points

Turning points in degree 2 polynomial (quadratic)

1 turning point

Max turning points in degree 3 polynomial (cubic)

Up to 2 turning points

Max turning points in degree 4 polynomial (quartic)

Up to 3 turning points

End behaviour of positive quartic graph

Starts top left, ends top right

End behaviour of positive x3x^3 coefficient cubic

Starts bottom left, ends top right

How curve behaves at single roots

Crosses the xx-axis

How curve behaves at double roots

Touches xx-axis and turns around

How curve behaves at triple roots

Flattens at the xx-axis

Definition of asymptotes

Lines graph approaches but never touches

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