What is the significance of the leading coefficient in a cubic function?

The leading coefficient determines the end behavior of the cubic function. If it is positive, the function rises to the right; if negative, it falls to the right.

How do you perform polynomial subtraction?

To perform polynomial subtraction, distribute the negative sign to the second polynomial and then combine like terms.

What is the vertex form of a cubic function?

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

What is the relationship between the roots and the factors of a polynomial?

The roots of a polynomial are the values of $$x$$ that make the polynomial equal to zero, and each root corresponds to a factor of the form $$(x - r)$$ .

How do you determine the number of turning points in a cubic function?

A cubic function can have up to two turning points, which occur where the first derivative changes sign.

What is the process of completing the square?

Completing the square involves rewriting a quadratic expression in the form $$(x - p)^2 + q$$ to make it easier to solve or graph.

What is the importance of the discriminant in polynomial equations?

The discriminant helps determine the nature of the roots of a polynomial equation. For a quadratic, it is given by $$b^2 - 4ac$$ .

How do you graph a cubic function?

To graph a cubic function, identify the roots, y-intercept, and turning points, then plot these points and sketch the curve.

Graphing, Factoring & Solving Cubic Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a cubic function?

Back

2.

FLASHCARD QUESTION

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

Back

3.

FLASHCARD QUESTION

Front

What does it mean to reflect a function over the x-axis?

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