Polynomial Functions Section 2 3 Objectives Find the

Polynomial Functions Section 2. 3

Objectives • Find the x-intercepts and y-intercept of a polynomial function. • Describe the end behaviors of a polynomial function. • Write the equation of a polynomial function given the zeros and a point on the function. • Determine the minimal degree of a polynomial given its graph. • Solve a word problem involving polynomial function.

Objectives • Use a graphing utility to find a local maximum or local minimum of a polynomial function. • Use a graphing utility to find the absolute maximum or absolute minumum of a polynomial function. • Use a graphing utility to find the intersection points of the graphs of two polynomials.

Vocabulary • • • polynomial function degree leading coefficient end behavior repeated zero multiplicity local minimum local maximum absolute minimum absolute maximum

Graph each of the following: positive leading coefficient and even degree

Graph each of the following: negative leading coefficient and even degree

Graph each of the following: positive leading coefficient and odd degree

Graph each of the following: negative leading coefficient and odd degree

For the function • Find the x-intercept(s). • Find the y-intercept(s). • Describe the end behaviors.

Find a possible formula for the polynomial of degree 4 that has a root of multiplicity 2 at x = 2 and roots of multiplicity 1 at x = 0 and x = -2 that goes through the point (5, 63).

What is the smallest possible degree of the polynomial whose graph is given below.

A box without a lid is constructed from a 36 inch by 36 inch piece of cardboard by cutting x inch squares from each corner and folding up the sides. • Determine the volume of the box as a function of the variable x. • Use a graphing utility to approximate the values of x that produce a volume of 3280. 5 cubic inches.

Consider the function: Find the absolute maximum and absolute minimum of the graph.