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

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Question 88249: Graph the following equation: y = –x^2 + 2x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph y=-x%5E2%2B2x, we need to plot some points.
We can start at any x value, so lets start at x=-2



y=-x%5E2%2B2x Start with the given polynomial


y=-%28-2%29%5E2%2B2%28-2%29 Plug in x=-2


y=-%284%29%2B2%28-2%29 Raise -2 to the second power to get 4


y=-%284%29%2B-4 Multiply 2 by -2 to get -4


y=-8 Now combine like terms

So our 1st point is (-2,-8)



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



y=-x%5E2%2B2x Start with the given polynomial


y=-%28-1%29%5E2%2B2%28-1%29 Plug in x=-1


y=-%281%29%2B2%28-1%29 Raise -1 to the second power to get 1


y=-%281%29%2B-2 Multiply 2 by -1 to get -2


y=-3 Now combine like terms

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



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



y=-x%5E2%2B2x Start with the given polynomial


y=-%280%29%5E2%2B2%280%29 Plug in x=0


y=-%280%29%2B2%280%29 Raise 0 to the second power to get 0


y=-%280%29%2B0 Multiply 2 by 0 to get 0


y=0 Now combine like terms

So our 3rd point is (0,0)



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



y=-x%5E2%2B2x Start with the given polynomial


y=-%281%29%5E2%2B2%281%29 Plug in x=1


y=-%281%29%2B2%281%29 Raise 1 to the second power to get 1


y=-%281%29%2B2 Multiply 2 by 1 to get 2


y=1 Now combine like terms

So our 4th point is (1,1)



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



y=-x%5E2%2B2x Start with the given polynomial


y=-%282%29%5E2%2B2%282%29 Plug in x=2


y=-%284%29%2B2%282%29 Raise 2 to the second power to get 4


y=-%284%29%2B4 Multiply 2 by 2 to get 4


y=0 Now combine like terms

So our 5th point is (2,0)



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



y=-x%5E2%2B2x Start with the given polynomial


y=-%283%29%5E2%2B2%283%29 Plug in x=3


y=-%289%29%2B2%283%29 Raise 3 to the second power to get 9


y=-%289%29%2B6 Multiply 2 by 3 to get 6


y=-3 Now combine like terms

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



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



y=-x%5E2%2B2x Start with the given polynomial


y=-%284%29%5E2%2B2%284%29 Plug in x=4


y=-%2816%29%2B2%284%29 Raise 4 to the second power to get 16


y=-%2816%29%2B8 Multiply 2 by 4 to get 8


y=-8 Now combine like terms

So our 7th point is (4,-8)


Now lets make a table of the values we have calculated 



 xy



 -2-8
 

 -1-3
 

 00
 

 11
 

 20
 

 3-3
 

 4-8
Now plot the points



Now connect the points to graph y=-x%5E2%2B2x