GUIDED NOTES – Lesson 3-5
Graphing Polynomial Functions
Name: ______________________ Period: ___
Objective: I can identify multiplicity in polynomial graphs and equations and apply to graphing.
Now we are ready to get a little more specific with
the graphs of polynomial functions, starting with
the different types of zeros/solutions/x-intercepts.
Remember that a zero is where the graph goes
through the x-axis, but remember it could also be
where the curve of the graph “______________”
the x-axis.
This brings us to MULTIPLICITY, which means the
same solution exists multiple times.
This particular graph has a zero with a multiplicity of 2 at x = -2,
so the zero written as a factor would be (
).
This solution in x = 3, it is just
written as a factor (
).
MULTIPLICITY GUIDE
EXAMPLES
Solution(s):
Degree:
Multiplicity of:
Direction:
Equation of this graph:
As a Factor:
Solution(s):
Degree:
Multiplicity of:
Direction:
Equation of this graph:
As a Factor:
Solution(s):
Degree:
Multiplicity of: As a Factor:
Direction:
Equation of this graph:
Now that you know how to pull factors and the equation out of a graph, you can reverse the process to sketch
graphs with much more accuracy than the previous lesson.
EXAMPLES: Graph the following equations in factored form.
e(x) = (x + 5)(x – 3)(x)
Degree:
Direction:
g(x) = -(x + 4)2(x + 1)(x – 2)3
Degree:
Direction: