Polynomial Graphs

Polynomial Graphs

Assessment

Flashcard

Mathematics

10th - 12th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 - 4x^2 + 3 is a polynomial.

2.

FLASHCARD QUESTION

Front

What does the term 'root' mean in relation to polynomials?

Back

A root of a polynomial is a value of x for which the polynomial equals zero. It is also known as a zero of the polynomial.

3.

FLASHCARD QUESTION

Front

What is meant by 'multiplicity' of a root?

Back

Multiplicity refers to the number of times a particular root appears in a polynomial. For example, if (x - 2) appears twice in the factorization, then 2 is a root with multiplicity 2.

4.

FLASHCARD QUESTION

Front

How does the multiplicity of a root affect the graph of a polynomial?

Back

If a root has an odd multiplicity, the graph will cross the x-axis at that root. If a root has an even multiplicity, the graph will touch the x-axis and bounce back.

5.

FLASHCARD QUESTION

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It determines the end behavior of the graph.

6.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in f(x) = 3x^4 + 2x^2 - 1, the degree is 4.

7.

FLASHCARD QUESTION

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial has an even degree if the highest power of the variable is an even number. The graph of such a polynomial will have the same end behavior on both sides.

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