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# given the system of equations y=x^2-4x x=4 the number of points of intersection is

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given the system of equations y=x^2-4x x=4 the number of points of intersection is

May 25, 2015

#4
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Melody, You use the "Input" line below the graph.  Just type in y=x^2-4*x and press Enter.  Similarly for x=4.

May 26, 2015

#1
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y = x² - 4x      x = 4

. . . I think this means when the lines cross. So the answer is 1 I think.

When x=4 . . . y = 4^2 - 4*4 = 0

Since y = x² - 4x is a parabola, it only ever crosses any x coordinate once. I think I'm making sense at least.

May 25, 2015
#2
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Hi Zac,

I didn't know that could be graphed in GeoGebra !

I use the download version - you seem to be using the online version, I wonder if it makes a difference?

Where did you go to graph the equations? I mean how did you do it?

May 25, 2015
#3
+981
+5

May 26, 2015
#4
+28029
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Melody, You use the "Input" line below the graph.  Just type in y=x^2-4*x and press Enter.  Similarly for x=4.

Alan May 26, 2015
#5
+101769
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Thanks Alan, I had never seen that input bar before

Anyway now, thanks to you and Zac, I have another cool tool!

Do you know if you can put restrictions on the domain or range?

like can I graph y=x^2   for  -3<x<2   ?

May 26, 2015
#6
+101424
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Yeah....thanks, Alan........I always wondered how to generate a graph in GeoGebra.......!!!!

May 26, 2015
#7
+101769
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Yes, me too Chris :)

May 26, 2015
#8
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You can put limits on as follows.  In the Input bar type:  If(-3<x<2,x^2,NaN)

This results in:

(I changed the colour myself - the default is black).

I should note:

1. The If statement is in the form If(condition, result if condition is true, result if condition is false);

2. NaN stands for Not A Number.

.

May 26, 2015
#9
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Thanks Alan, what does NaN stand for?

May 26, 2015
#10
+28029
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See my edit above.

NaN (Not A Number) is commonly used in many computer languages to represent an undefined region of a function.

.

May 26, 2015
#11
+101769
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Thanks Alan,  that is really neat.  I mean the true false condition.  I like that

May 26, 2015
#12
+101769
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I have just added this to the calculator/ other resources section of our Reference Material sticky thread.