6.1 - 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 parent function of cubic functions?

Back

The parent function of cubic functions is f(x) = x^3.

Front

What is the factored form of the polynomial function (x-2)(x-1)(x+1)(x+2)?

Back

The factored form is (x-2)(x-1)(x+1)(x+2).

Front

How do you factor the expression x² - 6x + 8?

Back

The expression factors to (x-2)(x-4).

Front

What is the range of all cube root functions in interval notation?

Back

The range of all cube root functions is (−∞, ∞).

Front

Describe the transformation of the graph y = -(x - 4)³ + 5.

Back

The graph is reflected over the x-axis, shifted right 4 units, and shifted up 5 units.

Front

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

Back

The graph of a cubic function has an 'S' shape, with one or two turning points.

Front

What is the leading coefficient in a cubic function?

Back

The leading coefficient is the coefficient of the highest degree term (ax^3) and determines the end behavior of the graph.

Front

How do you find the x-intercepts of a cubic function?

Back

To find the x-intercepts, set the cubic function equal to zero and solve for x.

Front

What is the significance of the discriminant in cubic functions?

Back

The discriminant helps determine the nature and number of roots of the cubic equation.