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## Project #3 -Benchmarks

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**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**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**GROUP NAME_________________**• Leader Name _________________ • Recorder Name________________ • Presentation Leader_____________ • All members must check over answers**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**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**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**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**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**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**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**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**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**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**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**MORE Parabola’s examplePAGE 13What is the vertex of the**following parabola: y = (x + 3)² + 4 • The vertex is the point (-3,4)**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.**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**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**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 •**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**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 •**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**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**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**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**Student Equation 1____________**• Draw Graph here:**Student Equation 2____________**• Draw Graph here:**Student Equation 3____________**• Draw Graph here:**Student Equation 4____________**• Draw Graph here:**Student Equation 5____________**• Draw Graph here:**Student Equation 6____________**• Draw Graph here:**Student Equation 7____________**• Draw Graph here:**Student Equation 8____________**• Draw Graph here:**Student Equation 9____________**• Draw Graph here:**Student Equation 10____________**• Draw Graph here:**Student Equation 11____________**• Draw Graph here:**Student Equation 12____________**• Draw Graph here:**Student Equation 13____________**• Draw Graph here:**Student Equation 14____________**• Draw Graph here:**Student Equation 15____________**• Draw Graph here:**Student Equation 16____________**• Draw Graph here:**Student Equation 17____________**• Draw Graph here:**Student Equation 18____________**• Draw Graph here:**Student Equation 19____________**• Draw Graph here:**Student Equation 20____________**• Draw Graph here:**Student Equation 21____________**• Draw Graph here:**Student Equation 22____________**• Draw Graph here:**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