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 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 Functions Page 1 website modules/solveabs.htm 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 Graph Page 2 y = |x| -FAMILY GRAPH A 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 6 y = ax 2 + bx + c Real-Life pictures of parabolas 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 x 2 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

Parabolic Functions UPS/DOWNS-page 7

Parabolas page 8 Narrow or Wide If |a| 1). Example: y = 0.5x 2 Example: y =5x 2

Parabolas y = x 2 -2 page 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 = x 2 +4 page 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 = - x 2 +3 page 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 = - x 2 -1 page 12 The graph is turn UPSIDE DOWN “U” shape on the y axis, but pushed upward because of the 3 (so +3 units down)

MORE Parabola’s example PAGE 13 What 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 -3 page 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 -3 page 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:

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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