Cubic Graphs Flashcards

A function of the form y = ax³ + bx² + cx + d, where a, b, c, and d are constants, and a ≠ 0.

A cubic graph has an 'S' shape or a reverse 'S' shape, depending on the sign of the leading coefficient (a).

If the coefficient of x³ (a) is positive, the graph starts in the bottom left and ends in the top right.

If the coefficient of x³ (a) is negative, the graph starts in the top left and ends in the bottom right.

A cubic graph can have up to two turning points, but it may also have none.

The roots are the x-values where the graph crosses the x-axis. A cubic graph can have 1, 2, or 3 real roots.

The y-intercept is the point where the graph crosses the y-axis, given by the constant term d in y = ax³ + bx² + cx + d.

Cubic graphs do not have line symmetry but may have rotational symmetry about a point.

The gradient of a cubic graph changes throughout the graph, increasing or decreasing depending on the section of the curve.

To sketch a cubic graph, identify the roots, y-intercept, turning points, and the general shape based on the sign of a.