The first column shows a sequence of numbers. Second column shows the first difference. (-6) – (-4) = -2 If the pattern continues, what is the 8 th number.

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Presentation transcript:

The first column shows a sequence of numbers. Second column shows the first difference. (-6) – (-4) = -2 If the pattern continues, what is the 8 th number in the first column? 1074

Polynomial Functions 5-1 Unit Objectives: Solve polynomial equations Identify function attributes: domain, range, degree, relative maximums/minimums, zeros Write and graph polynomial functions Model situations with polynomial functions Today’s Objective: I can describe polynomial functions.

Polynomial Function: Standard Form Polynomial: sum of monomials (terms) Degree of a polynomial: highest exponent Standard form: terms arranged by exponents in descending order

Classifying Polynomial By its DegreeExamplesBy the number of terms DegreeName# of termsName n Constant Linear Quadratic Cubic Quartic Quintic n th degree Monomial Binomial Trinomial polynomial of n terms Write in standard form. Classify by degree & Terms quartic polynomial of 4 terms n

End Behavior and Turning Points 1.Graph on your calculator window: [-5, 5, 1, -5, 5, 1] 2.Graph each equation below 3.Sketch each graph in your notes End Behavior Leading coefficient Even Degree Odd Degree ↑ and ↑↓ and ↑ ↓ and ↓ ↑ and ↓ a > 0 a < 0 Turning Points: At most n – 1

Describing the shape of the graph Relative Minimum Relative Maximum End Behavior: Turning points: Increasing/decreasing intervals: Up and down (0.82, 1.09) (-0.82, -1.09) Decreasing: − ∞ to − 0.82 Increasing: − 0.82 to 0.82 Decreasing: to ∞ At most two Pg. 285: #8-36 even,