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).

Tags

CCSS.HSA.APR.B.3

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 (−∞, ∞).

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF.BF.B.3

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.

Tags

CCSS.HSF-IF.C.7C

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.