1. 5.2/5.9 Polynomial & Linear Factors
Learning goals
graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases
graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior

2. The following are equivalent statements about a real number b and a polynomial P(x):
(x – b) is a factor of P(x)
b is a zero of the function
b is a root (or solution) of P(x) = 0
b is an x-intercept of the graph

3. So, for example… Equivalent Statements about Polynomials
– 4 is a solution of
– 4 is an x-intercept of the graph
– 4 is a zero of
(x + 4) is a factor of

4. Ex 1
Find the zeros, graph, find relative max/min.

5. Ex 2
Find the zeros, graph, find relative max/min

6. Ex 3
Write an equation in standard form with zeros at

7. Vocabulary
multiple zero : a repeated zero of a polynomial that occurs because of a repeated linear factor multiplicity : the number of times a zero occurs in a polynomial

8. Ex 4
For the following polynomial, find any multiple zeros and state the multiplicity of each

9. Transformation Types Review
reflection
horizontal shift
vertical shift
stretch/compression
Power Function

10. Ex 5
What is the equation of the following function that has been translated down 1 unit, left 6 units, and vertically stretched by a factor of 3 ?

11. Ex 6
What is the equation of the following function that has been reflected over the x- axis, translated up 2 units, right 3 units, and vertically compressed by a factor of ½ ?