5.1 Polynomial FunctionsPart 2

Describing the Shape of a Cubic Function1. List the function in standard

form2. Describe the end behavior of the

graph3. Determine the possible number

of turning points4. Use a Table to plot points5. Determine increasing and

decreasing intervals

Example: Describe the Shape of a Cubic Function

x y

-2

-1

0

1

2

Example: Describe the Shape of a Cubic Function

x y

-2

-1

0

1

2

Determine the sign of the leading coefficient and the degree of the polynomial.

1. Identify the end behaviorThis tells you whether the leading coefficient a is positive or negative

2. Identify the number of turning points

# of turning points + 1 = possible degree of the polynomial

Determine the sign of the leading coefficient and the least possible degree of the polynomial.

Determine the sign of the leading coefficient and the least possible degree of the polynomial.

Using differences to determine degreeGiven a table of values (or a set of

ordered pairs)Analyze the differences of consecutive

y – values, to determine the least-degree polynomial function that could generate the data◦ If the first differences are constant, the

function is linear◦ If the second differences are constant, the

function is quadratic◦ If the third differences are constant, the

function is cubic◦And so on…

Example: Determine the degree of the polynomial function with the given data.

Example: Determine the degree of the polynomial function with the given data.

HomeworkP 285 #32 – 39, 41 – 49all, 58