5.1 Polynomial Functions

P280-284

Standard form of a polynomial function: Terms are arranged by degree in descending numerical order.

Degree Name # Terms Name

0 Constant 1 Monomial1 Linear 2 Binomial2 Quadratic 3 Trinomial3 Cubic N Polynomial4 Quartic5 QuinticN Nth degree

Ex) Write in standard form. Then classify by degree and number of terms.

a)

b)

593 2 xx

121064 242 xxxx

N even N oddPositive a Up – up Down – upNegative a Down - down Up - down

Ex) What is the end behavior of the graph?

a)

b)

xxy 34 3

2882 234 xxxy

Maximum # turning points : n-1,where n is the degree

Turning point : change in the direction in terms of y…from increasing to decreasingor from decreasing to increasing.

Ex) Describe the shape of the graph,Including end behavior, turning points, and increasing/decreasing intervals.

a) 3

2

1xy

Ex) Describe the shape of the graph,Including end behavior, turning points, and increasing/decreasing intervals.

b) 23 xxy

Ex) Determine the degree of the polynomial by using differences..

X Y

-3 -1

-2 -7

-1 -3

0 5

1 11

2 9

3 -7