A13 - Cubic Functions

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, typically expressed in the form: f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is the general shape of a cubic function's graph?

Back

The graph of a cubic function can have one or two turning points and can extend to positive or negative infinity in both directions. It typically has an 'S' shape.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph intersects the y-axis, which occurs when x = 0.

Front

How do you find the y-intercept of a cubic function?

Back

To find the y-intercept of a cubic function, substitute x = 0 into the function and solve for y.

Front

What does the leading coefficient of a cubic function determine?

Back

The leading coefficient (the coefficient of the x^3 term) determines the end behavior of the cubic function's graph. If it's positive, the graph rises to the right; if negative, it falls to the right.

Front

What is a turning point in a cubic function?

Back

A turning point is a point on the graph where the function changes direction from increasing to decreasing or vice versa.

Front

What is the significance of the roots of a cubic function?

Back

The roots (or zeros) of a cubic function are the x-values where the function equals zero. They represent the x-intercepts of the graph.

Front

How can you find the roots of a cubic function?

Back

Roots can be found using factoring, synthetic division, or numerical methods such as the Rational Root Theorem or graphing.

Front

What is the difference between a cubic function and a quadratic function?

Back

A cubic function is of degree three and can have up to three roots, while a quadratic function is of degree two and can have up to two roots.

Front

What is the vertex form of a cubic function?

Back

The vertex form of a cubic function is expressed as f(x) = a(x - h)^3 + k, where (h, k) is the vertex of the graph.