graphing polynomial and absolute value functions by: jessica gluck
TRANSCRIPT
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Graphing Polynomial and Absolute Value
Functions
Graphing Polynomial and Absolute Value
FunctionsBy: Jessica GluckBy: Jessica Gluck
![Page 2: Graphing Polynomial and Absolute Value Functions By: Jessica Gluck](https://reader036.vdocument.in/reader036/viewer/2022072017/56649f055503460f94c1a08b/html5/thumbnails/2.jpg)
Definitions for Graphing Absolute Value FunctionsDefinitions 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.
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.
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Example of an Absolute Value GraphExample of an Absolute Value GraphFunction: 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.
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
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(Vertex)
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Definitions for Graphing Polynomial Functions
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 x-intercepts, and plug them back into the equation to find y.
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 x-intercepts, and plug them back into the equation to find y.
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Example 1 of a Polynomial GraphExample 1 of a Polynomial GraphFunction: 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.
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.
QuickTime™ and a decompressor
are needed to see this picture.
x y
-4 -6
-2 2, 2/3
-1 3
0 2
1 2/3
3 1
4 4,2/3
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Example 2 of a Polynomial GraphExample 2 of a Polynomial GraphFunction: 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.
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.
QuickTime™ and a decompressor
are needed to see this picture.
x y-2 -16
0 4
1 2
3 4
4 20
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Helpful HintsHelpful 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/Graphing-
Polynomial-Functions.topicArticleId-38949,articleId-38921.html http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_alge
bra/col_alg_tut35_polyfun.htm http://www.purplemath.com/modules/graphing3.htm
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/Graphing-
Polynomial-Functions.topicArticleId-38949,articleId-38921.html http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_alge
bra/col_alg_tut35_polyfun.htm http://www.purplemath.com/modules/graphing3.htm