Graphing
Polynomial and
Absolute Value
Functions
By: Jessica Gluck
Definitions for Graphing
Absolute Value Functions
 Vertex- The highest or lowest point on the
graph of an absolute value function. The
vertex of the graph of f(x)= lxl is 0,0.
 To get the x and y coordinates (vertex) of an
Absolute Value Equation, you take -x, and y.
(Example: For the equation y= Ix+4I -5; x= -4,
and y=-5.)
 Then, you plot the vertex. The graph either
increases by 1,1 and points up, or decreases
by 1,1 and points down. This depends on
weather the equation is negative or positive.
Example of an Absolute Value Graph
Function: Y= -Ix-2I -1.
Vertex: (x=2, y=-1)
We know that the graph is going to point down, because
the first variable is negative.
QuickTime™ and a
decompressor
are needed to see this picture.
(Vertex)
Definitions for Graphing
Polynomial Functions
 Turning Points: An important characteristic
of graphs of polynomial functions is that
they have turning points corresponding to
local maximum and minimum values.
 To find the two starting x-intercepts, take
the x values from the equation, and put 0 for
y.
 Then, find points between and beyond the xintercepts, and plug them back into the
equation to find y.
Example 1 of a Polynomial Graph
Function: f(x) = 1/6(x+3)(x-2)2
Plot the intercepts. Because -3 and 2 are zeros of f, plot
(-3,0) and (2,0). Then, plot points between and
beyond the x-intercepts.
x
y
-4
-6
-2
2, 2/3
-1
3
0
2
1
2/3
3
1
4
4,2/3
QuickTime™ and a
decompressor
are needed to see this picture.
Example 2 of a Polynomial Graph
Function: g(x) = (x-2)2(x+1)
Plot the intercepts. Because -2 and 1 are zeros of f, plot
(2,0) and (-1,0). Then, plot points between and
beyond the x-intercepts.
x
y
-2
-16
0
4
1
2
3
4
4
20
QuickTime™ and a
decompressor
are needed to see this picture.
Helpful Hints
 If the leading coefficient is positive, the two sides will go up.
If the leading coefficient were negative, the two sides will go
down.
 If the function has a leading term that has a positive
coefficient and an odd exponent, the function will always go
up toward the far right and down toward the far left.
 If the leading coefficient was negative with an odd exponent,
the graph would go up toward the far left and down toward
the far right.
For more help Go To:
 http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Grap
hing-Polynomial-Functions.topicArticleId-38949,articleId38921.html
 http://www.wtamu.edu/academic/anns/mps/math/mathlab/
col_algebra/col_alg_tut35_polyfun.htm
 http://www.purplemath.com/modules/graphing3.htm