Unit 3: Investigation 3A
Name: ______Period______
PART 1:
You can draw a tree by connecting, in order, the following points.
(1, 1), (2.5, 3), (2, 3), (3.5, 5), (3, 5), (4, 7), (5, 5), (4.5, 5), (6, 3), (5.5, 3), (7, 1), (1, 1)
a.)With you partner/group, plot the points above and connect in order.b.)For each point on the tree, add 2 to the x-coordinate. For instance, (1, 1) becomes (3, 1). Plot all of the new points on the same coordinate plane above and connect the resulting points in order.
Sasha and Tony plot three points on a coordinate plane and connect them to form a triangle.
Sasha:Let’s apply a rule to the coordinates of the triangle and see what happens to it.
Tony:Okay! How about if we use (x, y)(x -2, y + 4)?
With your partner/group, find the new values of T, R, and I (which we will call T’, R’, and I’) and plot them on the graph above.T (___, ___)T’ (___,___)
R (___, ___)R’ (___,___)
I (___, ___) I’ (___,___)
Describe the transformation. Use the words right/left and up/down in your description.
3A.03/3A.04
PART 1:
The graph of 2x + 3y = 12 is a line.
There are 2 points labeled on the line and 2 points labeled that are not on the line.
With your partner/group: How can we use the equation of the line to determine if a point is ON the line or NOT? Show using one point that is on the line and one that is not on the line to validate your determination.Point that is on the line
2( ) + 3( ) = 12 / Point not on the line
2( ) + 3( ) = 12
3A.03/3A.04
PART 2:
Tony:My book says that the graph of an equation is defined as the collection of all points with the coordinates that make the equation true.
Sasha:Yes, we saw this with the graph of2x + 3y = 12. All the points on the line made the equation true.
Tony:Right! However, how do I graph equations like y =- 1? We are supposed to find points that make the equation true and graph them, however there is no x for me to plug values into.
Sasha:Oh man, I have no idea! And what about x=3? Can we graph equations without a y?
With your partner/group, consider Tony and Sasha’s conversation and the equations to determine if you think they can graph the equations. If you feel they can, then create a strategy for graphing y=# or x=# equations, graph the equation, and thoroughly explain your strategy and reasoning. If you do not feel they can graph the equations, explain your reasoning.3A.03/3A.04
PART 3:
Sasha is working through her algebra homework. Tony walks over to ask for some help.
TONY:How do you find the graph of this equation?
Tony points to the equation y = x2-4x + 3 .
SASHA:Plug in different values of x. Try x = 0.
y = x2-4x + 3
y=(0)2-4(0) +3
TONY:0 is a good one to start with. All those zeros go away, since (0)2=0 and -4(0)=0.
SASHA:Right, and we get this.
y=(0)2-4(0) +3
y = 0 – 0 +3
y=3
TONY:y = 3? Now what do I do with the 3?
With your partner/group, what should Tony and Sasha do with the 3? What does the 3 represent?Use the following values of x to find more values of y and display your results in the table and graph below.
x / y = x2- 4x + 3 / y / (x, y)
-1
0
1
2
3
4
?
HINT: IF YOU ARE STILL UNSURE OF HOW TO DRAW THE SHAPE TRY SOME MORE POINTS THAT WILL HELP TO REVEAL MORE OF WHAT THE SHAPE LOOKS LIKE. USING A DECIMAL OR A FRACTION HELPS IN THIS PROBLEM. IT IS UP TO YOU TO FIND OUT WHAT THAT DECIMAL IS.
3A.06
The graph of y = x2 – 1 and y = 3 are graphed below.
With your partner/group, identify the points of intersection. How are these points related to the equations of each graph? Use the words satisfies in your explanation.Points of Intersection: (___, ___) (___, ___)
Relationship between points and equations?
Show that the points work by plugging in and making sure that they satisfy both equations.
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J. Olivier-SDUSD, rev 8-14-14 Adapted from CME Integrated I textbook