SOLUTION: I am having a difficult time with this equation and graphing it. y=x^2-4x

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Question 125371: I am having a difficult time with this equation and graphing it. y=x^2-4x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph y=x%5E2-4x, we need to plot some points.

We can start at any x value, so lets start at x=-1




Lets evaluate f%28-1%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%28-1%29=%28-1%29%5E2-4%28-1%29 Plug in x=-1


f%28-1%29=%281%29-4%28-1%29 Evaluate %28-1%29%5E2 to get 1

f%28-1%29=1%2B4 Multiply -4 and -1 to get 4

f%28-1%29=5 Now combine like terms


So when x=-1, f%28x%29=5



-------Now lets find another point-------



Lets evaluate f%280%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%280%29=%280%29%5E2-4%280%29 Plug in x=0


f%280%29=%280%29-4%280%29 Evaluate 1%280%29%5E2 to get 10

f%280%29=00 Multiply -4 and 0 to get 0

f%280%29=0 Now combine like terms


So when x=0, f%28x%29=0



-------Now lets find another point-------



Lets evaluate f%281%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%281%29=%281%29%5E2-4%281%29 Plug in x=1


f%281%29=%281%29-4%281%29 Evaluate 1%281%29%5E2 to get 11

f%281%29=1-4 Multiply -4 and 1 to get -4

f%281%29=-3 Now combine like terms


So when x=1, f%28x%29=-3



-------Now lets find another point-------



Lets evaluate f%282%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%282%29=%282%29%5E2-4%282%29 Plug in x=2


f%282%29=%284%29-4%282%29 Evaluate 1%282%29%5E2 to get 14

f%282%29=4-8 Multiply -4 and 2 to get -8

f%282%29=-4 Now combine like terms


So when x=2, f%28x%29=-4



-------Now lets find another point-------



Lets evaluate f%283%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%283%29=%283%29%5E2-4%283%29 Plug in x=3


f%283%29=%289%29-4%283%29 Evaluate 1%283%29%5E2 to get 19

f%283%29=9-12 Multiply -4 and 3 to get -12

f%283%29=-3 Now combine like terms


So when x=3, f%28x%29=-3



-------Now lets find another point-------



Lets evaluate f%284%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%284%29=%284%29%5E2-4%284%29 Plug in x=4


f%284%29=%2816%29-4%284%29 Evaluate 1%284%29%5E2 to get 116

f%284%29=16-16 Multiply -4 and 4 to get -16

f%284%29=0 Now combine like terms


So when x=4, f%28x%29=0



-------Now lets find another point-------



Lets evaluate f%285%29

f%28x%29=x%5E2-4x Start with the given polynomial


f%285%29=%285%29%5E2-4%285%29 Plug in x=5


f%285%29=%2825%29-4%285%29 Evaluate 1%285%29%5E2 to get 125

f%285%29=25-20 Multiply -4 and 5 to get -20

f%285%29=5 Now combine like terms


So when x=5, f%28x%29=5


Now lets make a table of the values we have calculated 



 xy



 -15
 

 00
 

 1-3
 

 2-4
 

 3-3
 

 40
 

 55
Now plot the points



Now connect the points to graph y=x%5E2-4x (note: the more points you plot, the easier it is to draw the graph)