Graphing Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 - 4x + 7 is a polynomial.

Front

How do you determine if a polynomial is odd or even?

Back

A polynomial is even if all its terms have even degrees and odd if all its terms have odd degrees. If it has both, it is neither.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in f(x) = 4x^5 - 3x^2 + 2, the degree is 5.

Front

What does the end behavior of a polynomial describe?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as the input approaches positive or negative infinity.

Front

What is a y-intercept?

Back

The y-intercept of a polynomial is the point where the graph intersects the y-axis, found by evaluating the polynomial at x=0.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero. For example, if f(x) = x^2 - 4, then x=2 and x=-2 are zeros.

Front

What is multiplicity in relation to polynomial zeros?

Back

Multiplicity refers to the number of times a particular zero appears in a polynomial. For example, if (x - 3)^2 is a factor, then 3 is a zero with multiplicity 2.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or other methods.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree. It affects the end behavior of the polynomial's graph.

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

A polynomial of degree n can have up to n real zeros, counting multiplicities.