Review Graphing Polynomials

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 are the points where the graph intersects the x-axis.

Front

How do you find the zeros of the polynomial P(x) = (x+4)(x-3)(x-2)?

Back

Set each factor equal to zero: x+4=0 (x=-4), x-3=0 (x=3), x-2=0 (x=2). The zeros are x=-4, x=3, x=2.

Front

What is the significance of the maximum and minimum values of a polynomial graph?

Back

The maximum value is the highest point on the graph, while the minimum value is the lowest point. These points indicate the range of the polynomial function.

Front

How can you determine if a polynomial has a maximum or minimum value?

Back

You can determine this by analyzing the leading coefficient: if it's positive, the polynomial has a minimum; if negative, it has a maximum.

Front

What does it mean for a polynomial to be increasing or decreasing?

Back

A polynomial is increasing on an interval if the y-values rise as x-values increase, and decreasing if the y-values fall as x-values increase.

Front

How do you identify the intervals where a polynomial is increasing or decreasing?

Back

By finding the derivative of the polynomial and determining where it is positive (increasing) or negative (decreasing).

Front

What is the degree of a polynomial, and how does it affect the graph?

Back

The degree of a polynomial is the highest exponent of x. It affects the number of zeros and the end behavior of the graph.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots (including complex and repeated roots).

Front

How do you determine the number of zeros a polynomial function can have?

Back

The number of zeros is determined by the degree of the polynomial. A polynomial of degree n can have up to n real zeros.

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.