project #3 -benchmarks mad 141 describes, analyzes, and generalizes, relationships, patterns, and...

Project #3 -Benchmarks Project #3 -Benchmarks Project #3 -Benchmarks Project #3 -Benchmarks MAD 141 describes , analyzes, and generalizes, MAD 141 describes , analyzes, and generalizes,

relationships, patterns, and functions using words relationships, patterns, and functions using words symbols, variables, tables, and graphssymbols, variables, tables, and graphs

MAD 142 determines the impact when changing MAD 142 determines the impact when changing parameters of given functions. parameters of given functions.

MAD 241 represents real-world problem situations MAD 241 represents real-world problem situations using finite graphs, matrices, sequences, series and using finite graphs, matrices, sequences, series and

recursive relations. recursive relations. MAD 242 uses systems of equations and inequalities MAD 242 uses systems of equations and inequalities

to solve real-world problems graphically, to solve real-world problems graphically, algebraically, and with matrices algebraically, and with matrices

Project #3 –Cooperative Project #3 –Cooperative LearningLearning

Project #3 –Cooperative Project #3 –Cooperative LearningLearning

Matching Graphs to EquationsMatching Graphs to EquationsPARABOLAS, LINEAR EQUATION, ABSOLUTE PARABOLAS, LINEAR EQUATION, ABSOLUTE

VALUE VALUE (OVERVIEW of rules/examples)(OVERVIEW of rules/examples)

Book Sections 2.2-2.6 Linear EquationsBook Sections 2.2-2.6 Linear Equations2.7-Absolute Value2.7-Absolute Value

Parabolas-8.2Parabolas-8.2

GROUP NAME_________________

• Leader Name _________________

• Recorder Name________________

• Presentation Leader_____________• All members must check over

answers

Absolute Value FunctionsPage 1

website 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 6

y = ax 2 + bx + c Real-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

Parabolic Functions UPS/DOWNS-page 7

Parabolas page 8

Narrow 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 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 -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 4IF YOU NOTICETHE 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

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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