Graphing Polynomial and Absolute Value

Functions

Graphing Polynomial and Absolute Value

FunctionsBy: Jessica GluckBy: Jessica Gluck

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.

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

are needed to see this picture.

(Vertex)

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.

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

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

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