Graphing Polynomials. Total number of roots = __. Maximum number of real roots = . Maximum.

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Presentation transcript:

Graphing Polynomials

Total number of roots = __________________________________. Maximum number of real roots = ________________________________. Maximum number of turning points = __________________________________. Complex roots always occur in __________________________________.

How does multiplicity of roots affect the graph? 1.Even multiplicity: 2.Odd multiplicity:

Given f(x), find the following without using your calculator. Then graph. a) End Behavior: b) Maximum # of turning points: c) f(0): d) Zeros (give multiplicity):

Given f(x), find the following without using your calculator. Then graph. a) End Behavior: b) Maximum # of turning points: c) f(0): d) Zeros (give multiplicity):

Given f(x) find the following using your calculator. Then graph. a)End Behavior: b) Maximum # of turning points: c) Max(s)/Min(s): d) f(0): e) Zeros (give multiplicity):

Sketch a graph of the function described. 1.Cubic: negative leading term, 1 real zero 2.Quadratic: positive leading term, 1 distinct real zero 3.Quintic: positive leading term, 4 x-intercepts

Write a polynomial with the given zeros. 1.4, (degree 2) 3.

An open box is to be made from a square piece of material, 16 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides. a. Write a function representing the volume. b. Use your calculator to graph the function found in part a. Estimate the value of x that will for which the volume is at a maximum. x