SOLUTION: Graph y= x^2 - 2x

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Question 151077: Graph y= x^2 - 2x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Table of Contents:


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In order to graph y=x%5E2-2x, we need to plot some points.


Let's find y when x=-3
(Note: you can start with any x-value):


y=x%5E2-2x Start with the given equation.


y=%28-3%29%5E2-2%28-3%29 Plug in x=-3.


y=1%289%29-2%28-3%29 Square -3 to get 9.


y=9-2%28-3%29 Multiply 1 and 9 to get 9.


y=9%2B6 Multiply -2 and -3 to get 6.


y=15 Combine like terms.


So when x=-3, then y=15.


So we have the point .


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Let's find y when x=-2:


y=x%5E2-2x Start with the given equation.


y=%28-2%29%5E2-2%28-2%29 Plug in x=-2.


y=1%284%29-2%28-2%29 Square -2 to get 4.


y=4-2%28-2%29 Multiply 1 and 4 to get 4.


y=4%2B4 Multiply -2 and -2 to get 4.


y=8 Combine like terms.


So when x=-2, then y=8.


So we have the point .


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Let's find y when x=-1:


y=x%5E2-2x Start with the given equation.


y=%28-1%29%5E2-2%28-1%29 Plug in x=-1.


y=1%281%29-2%28-1%29 Square -1 to get 1.


y=1-2%28-1%29 Multiply 1 and 1 to get 1.


y=1%2B2 Multiply -2 and -1 to get 2.


y=3 Combine like terms.


So when x=-1, then y=3.


So we have the point .


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Let's find y when x=0:


y=x%5E2-2x Start with the given equation.


y=%280%29%5E2-2%280%29 Plug in x=0.


y=1%280%29-2%280%29 Square 0 to get 0.


y=0-2%280%29 Multiply 1 and 0 to get 0.


y=0%2B0 Multiply -2 and 0 to get 0.


y=0 Combine like terms.


So when x=0, then y=0.


So we have the point .


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Let's find y when x=1:


y=x%5E2-2x Start with the given equation.


y=%281%29%5E2-2%281%29 Plug in x=1.


y=1%281%29-2%281%29 Square 1 to get 1.


y=1-2%281%29 Multiply 1 and 1 to get 1.


y=1-2 Multiply -2 and 1 to get -2.


y=-1 Combine like terms.


So when x=1, then y=-1.


So we have the point .


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Let's find y when x=2:


y=x%5E2-2x Start with the given equation.


y=%282%29%5E2-2%282%29 Plug in x=2.


y=1%284%29-2%282%29 Square 2 to get 4.


y=4-2%282%29 Multiply 1 and 4 to get 4.


y=4-4 Multiply -2 and 2 to get -4.


y=0 Combine like terms.


So when x=2, then y=0.


So we have the point .


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Let's find y when x=3:


y=x%5E2-2x Start with the given equation.


y=%283%29%5E2-2%283%29 Plug in x=3.


y=1%289%29-2%283%29 Square 3 to get 9.


y=9-2%283%29 Multiply 1 and 9 to get 9.


y=9-6 Multiply -2 and 3 to get -6.


y=3 Combine like terms.


So when x=3, then y=3.


So we have the point .


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Let's find y when x=4:


y=x%5E2-2x Start with the given equation.


y=%284%29%5E2-2%284%29 Plug in x=4.


y=1%2816%29-2%284%29 Square 4 to get 16.


y=16-2%284%29 Multiply 1 and 16 to get 16.


y=16-8 Multiply -2 and 4 to get -8.


y=8 Combine like terms.


So when x=4, then y=8.


So we have the point .


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Now let's make a table of the values we just found.


Table of Values:





xy
-315


-28


-13


00


1-1


20


33


48

Now let's plot the points:







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Graph:


Now draw a curve through all of the points to graph y=x%5E2-2x:


Graph of y=x%5E2-2x