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Polynomial Functions. PPT 2.3.1. Polynomial Functions. The largest exponent within the polynomial determines the degree of the polynomial. Explore Polynomials. Linear Function. Quadratic Function. Cubic Function. Quartic Function. Leading Coefficient.

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Presentation Transcript
polynomial functions1
Polynomial Functions

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

explore polynomials
Explore Polynomials

Linear Function

Quadratic Function

Cubic Function

Quartic Function

leading coefficient
Leading Coefficient

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.

cubic polynomials
Graph A

Graph B

Cubic Polynomials

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?

cubic polynomials1
Cubic Polynomials

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

cubic polynomials2
Cubic Polynomials

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

cubic polynomials3
Cubic Polynomials

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

quartic polynomials
Graph A

Graph B

Quartic Polynomials

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?

quartic polynomials1
Quartic Polynomials

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

quartic polynomials2
Quartic Polynomials

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

quartic polynomials3
Quartic Polynomials

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

quartic polynomials4
Quartic Polynomials

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

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