SOLUTION: Graph the equations. (1) y = x squared - 4x (2) y = -x + 1

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Question 122812: Graph the equations.
(1) y = x squared - 4x
(2) y = -x + 1
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
# 1

In order to graph , we need to plot some points. To do that, we need to plug in some x values to get some y values


So let's find the first point:



Start with the given function


Plug in


Raise -2 to the 2nd power to get 4


Multiply 1 and 4 to get 4


Multiply 4 and -2 to get -8


Subtract -8 from 4 to get 12


So when , we have


So our 1st point is (-2,12)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise -1 to the 2nd power to get 1


Multiply 1 and 1 to get 1


Multiply 4 and -1 to get -4


Subtract -4 from 1 to get 5


So when , we have


So our 2nd point is (-1,5)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise 0 to the 2nd power to get 0


Multiply 1 and 0 to get 0


Multiply 4 and 0 to get 0


Subtract 0 from 0 to get 0


So when , we have


So our 3rd point is (0,0)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise 1 to the 2nd power to get 1


Multiply 1 and 1 to get 1


Multiply 4 and 1 to get 4


Subtract 4 from 1 to get -3


So when , we have


So our 4th point is (1,-3)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise 2 to the 2nd power to get 4


Multiply 1 and 4 to get 4


Multiply 4 and 2 to get 8


Subtract 8 from 4 to get -4


So when , we have


So our 5th point is (2,-4)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise 3 to the 2nd power to get 9


Multiply 1 and 9 to get 9


Multiply 4 and 3 to get 12


Subtract 12 from 9 to get -3


So when , we have


So our 6th point is (3,-3)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise 4 to the 2nd power to get 16


Multiply 1 and 16 to get 16


Multiply 4 and 4 to get 16


Subtract 16 from 16 to get 0


So when , we have


So our 7th point is (4,0)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise 5 to the 2nd power to get 25


Multiply 1 and 25 to get 25


Multiply 4 and 5 to get 20


Subtract 20 from 25 to get 5


So when , we have


So our 8th point is (5,5)


-------------- Let's find another point --------------


Start with the given function


Plug in


Raise 6 to the 2nd power to get 36


Multiply 1 and 36 to get 36


Multiply 4 and 6 to get 24


Subtract 24 from 36 to get 12


So when , we have


So our 9th point is (6,12)


Now lets make a table of the values we have calculated 



 xy



 -212
 

 -15
 

 00
 

 1-3
 

 2-4
 

 3-3
 

 40
 

 55
 

 612
Now plot the points



Now connect the points to graph (note: the more points you plot, the easier it is to draw the graph)









# 2





Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is


Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means


Also, because the slope is , this means:




which shows us that the rise is -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1



So starting at , go down 1 unit


and to the right 1 unit to get to the next point



Now draw a line through these points to graph

So this is the graph of through the points and
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