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Notes Day 6.1

Notes Day 6.1. Classify Polynomials Study End Behavior Fundamental Theorem of Algebra. Classify Polynomials. 1. 0. Constant. Monomial. 1. 2. Binomial. Linear. 2. 1. Monomial. Quadratic. 3. 3. Cubic. Trinomial. 4. 2. Quartic. Binomial. 5. 4. Quintic. Polynomial.

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Notes Day 6.1

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  1. Notes Day 6.1 Classify Polynomials Study End Behavior Fundamental Theorem of Algebra

  2. Classify Polynomials 1 0 Constant Monomial 1 2 Binomial Linear 2 1 Monomial Quadratic 3 3 Cubic Trinomial 4 2 Quartic Binomial 5 4 Quintic Polynomial

  3. Polynomial Graph End Behavior SAME Even: Left end __________ behavior Odd: Left end ____________ behavior Assume this is the leading term of a polynomial in standard form. OPPOSITE axn n – 1 __________ max turns UP Positive: Right end _____________ Negative: Right end ____________ DOWN

  4. Up 2 Down 3 Down Down Up Down 2

  5. Which is possible for this graph according to end behavior? y= -3x5 + 4x + 1 y = -2x4 + 1 y = 3x2 + 4x + 1 y = 2x5 + 4x + 1

  6. Write a polynomial function in standard form with zeros at -2,-5, and 3. Then classify it by degree and term. (x+2) (x+5) (x – 3) Y = X3 + 4x2 – 11x – 30 (x2 + 7x + 10) (x – 3) Cubic Polynomial • GRAPH THIS ON BACK OF YOUR NOTES… • Plot roots • Use leading term to identify end behavior • Use 2nd trace to find max and min between roots 10x 7x2 x3 -30 -21x -3x2

  7. FundamentalTheorem of AlgebraThe roots of polynomial functions are complex numbers Irrationals Rationals Integers Wholes Counting ½ , -3.4, 1/3 -2, -1, 0, 1, 2, 0, 1 ,2 ,3 ,4 ,… 1 ,2 ,3 ,4 ,…

  8. Draw a possible quartic function with a negative leading coefficient, 2 real roots at and a y-intercept of 2. The last part of the graph can vary greatly! Due to quartic (4th degree – there can be a max of 3 turns

  9. Review Parent Functions / Shifts D: [-1,∞) R: [-2,∞) Yes (-1,-2) D: (-∞,∞) R: (-∞ -5] (4,-5) Yes D: (-∞,∞) R: [-4,∞) Yes (3,-4) D: (-∞,∞) R: (-∞,∞) Yes

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