1. Graphing Polynomial and Absolute Value Functions By: Jessica Gluck

2. 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.  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.

3. 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. 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. (Vertex)

4. 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.

5. 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. 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. xy -4-6 -22, 2/3 3 02 12/3 31 44,2/3

6. 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. 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. xy -2-16 04 12 34 420

7. 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/Gra phing-Polynomial-Functions.topicArticleId-38949,articleId- 38921.html  http://www.wtamu.edu/academic/anns/mps/math/mathlab/ col_algebra/col_alg_tut35_polyfun.htm http://www.wtamu.edu/academic/anns/mps/math/mathlab/ col_algebra/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/Gra phing-Polynomial-Functions.topicArticleId-38949,articleId- 38921.html  http://www.wtamu.edu/academic/anns/mps/math/mathlab/ col_algebra/col_alg_tut35_polyfun.htm http://www.wtamu.edu/academic/anns/mps/math/mathlab/ col_algebra/col_alg_tut35_polyfun.htm  http://www.purplemath.com/modules/graphing3.htm