38 > 22. Do Now Solve the inequality and come up with a real world scenario that fits the solution.

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Presentation transcript:

Do Now Solve the inequality and come up with a real world scenario that fits the solution.

38 > 22

5.1 Polynomial Functions Learning goals graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

5.1 Polynomial Functions Vocabulary monomial : a number, a variable, or the product of a real number and variables with whole number exponents polynomial : a monomial or the sum of monomials degree : For a monomial – the sum of its exponents For a polynomial – the largest sum of exponents from a term **Always put answers in standard form: descending order of exponents

Classifying Polynomials Shape By Degree 0 – constant 1 – linear 2 – quadratic 3 – cubic 4 – quartic 5 – quintic By # of Terms 1 – monomial 2 – binomial 3 – trinomial 4 or more - polynomial

Ex 1 Put in standard form What is the degree of the polynomial? Classify each polynomial by degree and number of terms What shape is it?

Ex 2 Write in standard form, classify, state degree and shape.

Vocabulary The degree of a polynomial function affects the shape of its graph the maximum number of turning points the way behaves at its ends turning point : places where a graph changes direction end behavior : direction of the graph where the arrows appear (far left and far right of the graph)

Vocabulary relative minimum /relative maximum peaks and valleys within the graph of a polynomial that has several turning points

Ex 3 Find the relative minimum and maximum

End Behavior a is positive is negative behaves like n is even (n≠0) parabola n is odd line

Ex 4 Describe the end behavior Is the graph odd or even? Is the leading coefficient positive or negative? Relative max or min?

Ex 5 Describe the end behavior Is the graph odd or even? Is the leading coefficient positive or negative? Relative max or min?

Ex 6 For each polynomial function: describe the end behavior sketch

Ex 7 For each polynomial function: describe the end behavior sketch

WS 5.1 Homework