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Polynomial Functions

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Polynomial Functions

PPT 2.3.1

The largest exponent within the polynomial determines the degree of the polynomial.

Linear Function

Quadratic Function

Cubic Function

Quartic Function

The leading coefficient is the coefficient of the first term in a polynomial when the terms are written in descending order by degrees.

For example, the quartic function

f(x) = -2x4 + x3 – 5x2 – 10 has a leading coefficient of -2.

Graph A

Graph B

Look at the two graphs and discuss the questions given below.

1. How can you check to see if both graphs are functions?

- 2. How many x-intercepts do graphs A & B have?

3. What is the end behaviour for each graph?

4. Which graph do you think has a positive leading coeffient? Why?

5. Which graph do you think has a negative leading coefficient? Why?

The following chart shows the properties of the graphs on the left.

The following chart shows the properties of the graphs on the left.

The following chart shows the properties of the graphs on the left.

Graph A

Graph B

Look at the two graphs and discuss the questions given below.

1. How can you check to see if both graphs are functions?

- 2. How many x-intercepts do graphs A & B have?

3. What is the end behaviour for each graph?

4. Which graph do you think has a positive leading coeffient? Why?

5. Which graph do you think has a negative leading coefficient? Why?

The following chart shows the properties of the graphs on the left.

The following chart shows the properties of the graphs on the left.

The following chart shows the properties of the graphs on the left.

The following chart shows the properties of the graphs on the left.