Solving Polynomials by Graphing

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They represent the x-intercepts of the graph.

Front

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

Back

To find the y-intercept of a polynomial function, evaluate the function at x=0. The y-intercept is the point (0, f(0)).

Front

What is standard form of a polynomial?

Back

Front

How do you solve a quadratic equation by factoring?

Back

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity, determined by the leading term.

Front

What does it mean for a polynomial to have a multiplicity?

Back

Multiplicity refers to the number of times a particular zero appears in a polynomial. A zero with an even multiplicity touches the x-axis, while one with an odd multiplicity crosses it.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

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.

Front

How can you graph a polynomial function?

Back

To graph a polynomial function, identify the zeros, y-intercept, and end behavior, then plot these points and sketch the curve.

Front

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

Back