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Project #3 -Benchmarks

Project #3 -Benchmarks . MAD 141 describes , analyzes, and generalizes, relationships, patterns, and functions using words symbols, variables, tables, and graphs MAD 142 determines the impact when changing parameters of given functions.

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Project #3 -Benchmarks

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  1. Project #3 -Benchmarks MAD 141 describes , analyzes, and generalizes, relationships, patterns, and functions using words symbols, variables, tables, and graphs MAD 142 determines the impact when changing parameters of given functions. MAD 241 represents real-world problem situations using finite graphs, matrices, sequences, series and recursive relations. MAD 242 uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices

  2. Project #3 –Cooperative Learning Matching Graphs to Equations PARABOLAS, LINEAR EQUATION, ABSOLUTE VALUE (OVERVIEW of rules/examples) Book Sections 2.2-2.6 Linear Equations 2.7-Absolute Value Parabolas-8.2

  3. GROUP NAME_________________ • Leader Name _________________ • Recorder Name________________ • Presentation Leader_____________ • All members must check over answers

  4. Absolute Value FunctionsPage 1website http://www.purplemath.com/modules/solveabs.htm • You can, by the way, verify the above solution graphically. When you attempt to solve the absolute-value equation y =|x| , you are, in effect, setting two line equations equal to each other and finding where they cross. In this case, as you can see on next slide

  5. Absolute Value GraphPage 2y = |x|-FAMILY GRAPHA horizontal line y =3 is drawn to show the equal distance between the symmetric parts of the graphs

  6. Absolute Value Example 2 – page 3 • Y = |x|+2 means the graph will be the same as the family graph, but move up on the y-axis 2 units (see below) 2

  7. Absolute Value Example 3 – page 4 • Y = |x|-3 means the graph will be the same as the family graph, but move up on the y-axis 2 units (see below) -3

  8. Absolute Value Example 4 – page 5 • Y = -|x|-3 means the graph turn downward on the y-axis and the whole graph moves down to -3 units, (see below) -3

  9. Family Graphs-page 6y = ax 2 + bx + cReal-Life pictures of parabolas www.hip2b2.com/news/ramps-and-other-real-life-parabolas/70017 • The above equation is the standard form of a parabola equation and is generally expressed this way: Positive a in front of the x2 directs the parabola up The role of 'a' • If a> 0, the parabola opens upwards –like a regular “U” • if a< 0, it opens downwards

  10. Parabolic Functions UPS/DOWNS-page 7

  11. Parabolas page 8Narrow or Wide • If |a| < 1, the graph of the graph becomes narrower(The effect is the opposite of |a| > 1). • Example: y = 0.5x2 Example: y =5x2

  12. Parabolas y = x2 -2page 9 • The graph is turn “U” shape up on the y axis, but pushed downward because of the -2 (so -2 units down) 2

  13. Parabolas y = x2 +4page 10 • The graph is turn “U” shape up on the y axis, but pushed upward because of the 4 (so +4 units down) 4

  14. Parabolas y = -x2 +3page 11 • The graph is turn UPSIDE DOWN “U” shape on the y axis, but pushed upward because of the 3 (so +3 units down) 3

  15. Parabolas y = -x2 -1page 12 • The graph is turn UPSIDE DOWN “U” shape on the y axis, but pushed upward because of the 3 (so +3 units down) -1

  16. MORE Parabola’s examplePAGE 13What is the vertex of the following parabola: y = (x + 3)² + 4 • The vertex is the point (-3,4)

  17. Parabols-Axis of Symmetry-page 14 • If a is positive, the parabola opens upward and has a minimum point.The axis of symmetry is x = (-b)/2a • If a is negative, the parabola opens downward and has a maximum point.The axis of symmetry is x = (-b)/2a.

  18. Linear Equations (AX + BY = c) -page 15 • Standard form of the Linear equations can be rewritten in the form of y = mx + b . • We call this form slope-intecept form

  19. Graph of Linear Equations- page 16 • The LINE RISES to the right, the slope is positive example • Y = 2/3 x + 2 where • Y intercept is 2, as you plug in (0) for x • Slope is 2/3 : rise 2 and go to the right 3

  20. Graph y = 2/3x + 2-page 17 • Place a point on the y- axis at your y-intercept 2 • Slope is 2/3 so rise 2 • Go the right 3 2 •

  21. Graph y = 2/3x -3page 18 • Place a point on the y- axis at your y-intercept -3 • Slope is 2/3 so rise 2 • Go the right 3 • 3

  22. Graph y = -3/4x -3page 19 • Place a point on the y- axis at your y-intercept -3 • Slope is -3/4 so go down 3 and to right 4 IF YOU NOTICE THE LINE FALLS TO THE RIGHT -3 •

  23. Y LINE MEANS Y = 6 IS HORIZONTAL –Page 20 • Y = 0X + 3 IS THE Slope – intercept form of the equation so the slope is “O” • Graph y = 3: 3

  24. Y LINE MEANS Y = 6 IS HORIZONTAL –Page 21 • Y = 0X - 5 IS THE Slope – intercept form of the equation so the slope is “O” • Graph y = -5: -5

  25. X Line means the lines is a Vertical Line-page 22 • Equation in slope intercept form is • X + 0y = 7 where • X = 7 • Graph 7

  26. X Line means the lines is a Vertical Line-page 23 • Equation in slope intercept form is • X + 0y = -2 where • X = -2 • Graph -2

  27. Student Equation 1____________ • Draw Graph here:

  28. Student Equation 2____________ • Draw Graph here:

  29. Student Equation 3____________ • Draw Graph here:

  30. Student Equation 4____________ • Draw Graph here:

  31. Student Equation 5____________ • Draw Graph here:

  32. Student Equation 6____________ • Draw Graph here:

  33. Student Equation 7____________ • Draw Graph here:

  34. Student Equation 8____________ • Draw Graph here:

  35. Student Equation 9____________ • Draw Graph here:

  36. Student Equation 10____________ • Draw Graph here:

  37. Student Equation 11____________ • Draw Graph here:

  38. Student Equation 12____________ • Draw Graph here:

  39. Student Equation 13____________ • Draw Graph here:

  40. Student Equation 14____________ • Draw Graph here:

  41. Student Equation 15____________ • Draw Graph here:

  42. Student Equation 16____________ • Draw Graph here:

  43. Student Equation 17____________ • Draw Graph here:

  44. Student Equation 18____________ • Draw Graph here:

  45. Student Equation 19____________ • Draw Graph here:

  46. Student Equation 20____________ • Draw Graph here:

  47. Student Equation 21____________ • Draw Graph here:

  48. Student Equation 22____________ • Draw Graph here:

  49. GROUP SCORING_____________ • EACH GROUP MEMBER WILL RECEIVE THE SAME SCORING • Maximum of 150 points for this Project • -10 EACH TIME CAUGHT OFF TASK • -10 for each graph not matching the equation • Excessive talking or distractions will result in the team missing this project grade and written up. PLEASE REMAIN FOCUSED

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