Sketching Polynomials (Edexcel A-Level Mathematics): Flashcards

A quartic graph has up to $3$ turning points.

A cubic polynomial has a degree of $3$.

Set $y = 0$: Solve $(x + 1)(x - 3) = 0$ for $x$.

Starts from top left and ends top right.

Set $x=0$; $f(0) = 1 \cdot 2 = 2$, so y-intercept is $(0, 2)$.

The curve touches the $x$-axis and turns around.

Starts at the top left and ends at the bottom right.

Check the sign of the coefficient of $x^4$.

A cubic graph has an 'S' shape, can be increasing or decreasing.

It is a parabola that opens upwards.