ALGEBRA II HONORS/GIFTED - SECTION 5-1 (Polynomial Functions) 2/28/2019 ALGEBRA II HONORS/GIFTED @ SECTION 5-1 : POLYNOMIAL FUNCTIONS

1) Fill in the chart. DEGREE NAME EXAMPLE 1 2 3 4 5

Write each polynomial in Standard Form Write each polynomial in Standard Form. Then, classify by degree and number of terms. 2) 3x3 – x + 5x4 4) 4x – 6x2 + x3 – 12 + 10x2 ANSWERS : 5x4 + 3x3 – x, quartic trinomial ANSWERS : x3 + 4x2 + 4x – 12, cubic polynomial 3) 2x2 – 4x5 ANSWERS : -4x5 + 2x2 + 13, quintic binomial

Determine the end behavior of the graph of each polynomial function Determine the end behavior of the graph of each polynomial function. (Hint : ) 5) y = x3 8) y = -x3 6) y = 2x3 – 4x + 3 9) y = -x3 + 2x2 + x - 2 7) y = x3 – 2x2 – x + 2 10) y = -2x3 + x + 4

+, even -, even +, odd -, odd 11) y = x4 + x3 + 2 15) Now, let’s make some generalizations. Leading Coefficient Left Right +, even -, even +, odd -, odd 12) y = x4 – x2 - 3 13) y = x3 – x4 + x - 4 14) y = 5 – x4 + x3

ANSWERS : down and up; there are no turning points; increases from Determine the shape of the graph of each cubic function including end behavior, turning points, and increasing/decreasing intervals. 16) y = -x3 + 12x 17) y = x3 ANSWERS : up and down; turning points at (-2, -16) and (2, 16); decreases from to -2, increases from -2 to 2, decreases from 2 to ANSWERS : down and up; there are no turning points; increases from to