Unit 3 Sections 1-3

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Unit 3 - Polynomials and Rational Functions

This chapter focuses on analyzing polynomials and rational functions, their roots, asymptotes . Use the graphics calculator to help you with the mechanics of this chapter.

Graphing Calculator Skills needed for this chapter.

Section 3.1 Quadratic Function

This section continues where the last chapter left off in the study of quadratics. It explores shifting and stretching of the curve along with vertices, axies of symmetry, maximums, minimums, roots (zeros) and comparison of the forms of the Quadratic Function.

f(x) = ax²+ bx + c vs. f(x) = a( x - h)² + k

You should be able to:

Use completing the square method to convert a quadratic function to standard form.
Click on the logo to explore completing the square

Find the vertex , axis of symmetry, y-intercepts, and zeros of a quadratic function.
Click on the logo to explore vertices
Click on the logo to explore intercepts, zeros, and symmetry

Predict the stretching, and shifting from a quadratic given in Standard form
Explore vertical and horizontal shifting
Click on the logo to explore shifting

Find the function, given the vertex and a random point.

Find the maximum or minimum of a parabolic function

(using -b/2a formula and the max min functions of the calculator.)

Click on the logo to explore Parabolas

Internet Link for Quadratic Functions

Click on the icon to explore Parabolas

Section 3.2 Polynomials of Higher Degree

This section explores polynomials of degree higher than 2. You will learn to analyze and explore of these functions graphically.

You should be able to:

Sketch the graph on a calculator adjusting the viewing windows to include relative maxima, minima, and zeros.

graph graph graph

Find a polynomial, given the zeros.

Dermine whether the function is odd or even and make assumptions about end behavior of the polynomial given the zeros.

Use the calculator to find relative maxima, minima, and zeros using the Intermediate Value Theorem.

Section 3.3 Real Zeros of Polynomial Functions

This section explains the methods used to find the real zeros of a polynomial function. Synthetic division is used repeatedly.

You should be able to:

divide polynomials using long division and synthetic division.

Use the remainder theorem to help factor a polynomial

Use the factor theorem to help find the zeros of a polynomial

Use the Rational Zeros Test to find the possible rational zeros

More info on finding zeros.

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