SOLUTION: Graph the following equation: y = –x^2 + x

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Question 88244: Graph the following equation: y = –x^2 + x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph y=-x%5E2%2Bx, we need to plot some points.
We can start at any x value, so lets start at x=-3



y=-x%5E2%2Bx Start with the given polynomial


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


y=-%289%29%2B%28-3%29 Raise -3 to the second power to get 9


y=-12 Now combine like terms

So our 1st point is (-3,-12)



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



y=-x%5E2%2Bx Start with the given polynomial


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


y=-%284%29%2B%28-2%29 Raise -2 to the second power to get 4


y=-6 Now combine like terms

So our 2nd point is (-2,-6)



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



y=-x%5E2%2Bx Start with the given polynomial


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


y=-%281%29%2B%28-1%29 Raise -1 to the second power to get 1


y=-2 Now combine like terms

So our 3rd point is (-1,-2)



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



y=-x%5E2%2Bx Start with the given polynomial


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


y=-%280%29%2B%280%29 Raise 0 to the second power to get 0


y=0 Now combine like terms

So our 4th point is (0,0)



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



y=-x%5E2%2Bx Start with the given polynomial


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


y=-%281%29%2B%281%29 Raise 1 to the second power to get 1


y=0 Now combine like terms

So our 5th point is (1,0)



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



y=-x%5E2%2Bx Start with the given polynomial


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


y=-%284%29%2B%282%29 Raise 2 to the second power to get 4


y=-2 Now combine like terms

So our 6th point is (2,-2)



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



y=-x%5E2%2Bx Start with the given polynomial


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


y=-%289%29%2B%283%29 Raise 3 to the second power to get 9


y=-6 Now combine like terms

So our 7th point is (3,-6)


Now lets make a table of the values we have calculated 



 xy



 -3-12
 

 -2-6
 

 -1-2
 

 00
 

 10
 

 2-2
 

 3-6
Now plot the points



Now connect the points to graph y=-x%5E2%2Bx