5.2 Notes
Evaluate and Graph Polynomials
Polynomial Function: All exponents are whole numbers & coefficients are real numbers.
Polynomial
Not a Polynomial
f ( x)  0.5x 2   x 1  4
f ( x)  x  4 x  3  2
1
f ( x)  2 x 2  x  4
2
3
2
f ( x)   x 3 2 x
f ( x)  3x  4 x 2  1
Standard Form of a Polynomial: Written in descending order from left to right.
f ( x)  10 x3  4 x 2  x  3
f ( x)  2 x2  4 x 4  5  2 x
Standard form:
Leading coefficient:
Degree of the polynomial:
Constant term:
Degree
0
1
2
3
4
Type
Constant
Linear
Quadratic
Cubic
Quartic
Standard Form
Example 1: Identify the polynomial by degree and type. Identify the leading coefficient.
A.) f ( x)  3x2  4 x3  7
B.) f ( x)  x 4 3x  1
3
2
C.) f ( x)  x 2   x  8
Example 2: Evaluate the polynomial using direct substitution.
A.) f ( x)  5x3  x2  4 x  1; x  4
B.) f ( x)  3x5  x4  5x  10; x  2
HW: p. 341 # 4 - 12, 24 - 31, 39, 41, 43, 47, 48
End Behavior of Polynomials: Direction of a graph as x   and x   .
Positive Leading Coefficient
Negative Leading Coefficient
f ( x)  x
f ( x)   x
Odd
degree
f ( x)  _____ as x  _____
f ( x)  _____ as x  _____
Even
degree
f ( x)  _____ as x  _____
f ( x)  _____ as x  _____
f ( x)  x2
f ( x)  _____ as x  _____
f ( x)  _____ as x  _____
f ( x)   x2
f ( x)  _____ as x  _____
f ( x)  _____ as x  _____
Example 4: Describe the end behavior of…
A.) f ( x)  3x8  4 x3
B.) f ( x)  8x3  9
f ( x)  _____ as x  _____
f ( x)  _____ as x  _____
C.) f ( x)  6 x3 10 x
f ( x)  _____ as x  _____
f ( x)  _____ as x  _____
Example 5: Use a table to graph
A.) f ( x)  x3  2 x2 1
f ( x)  _____ as x  _____
f ( x)  _____ as x  _____
B.) f ( x)   x4  3