SOLUTION: f(x) = -2x^2 - 8x + 3

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Question 130124: f(x) = -2x^2 - 8x + 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to graph?

In order to graph f%28x%29=-2x%5E2-8x%2B3, 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:



f%28x%29=-2x%5E2-8x%2B3 Start with the given function


f%28-5%29=-2%28-5%29%5E2-8%28-5%29%2B3 Plug in x=-5


f%28-5%29=-2%2A25-8%2A-5%2B3 Raise -5 to the 2nd power to get 25


f%28-5%29=-50-8%2A-5%2B3 Multiply -2 and 25 to get -50


f%28-5%29=-50--40%2B3 Multiply 8 and -5 to get -40


f%28-5%29=-10%2B3 Subtract -40 from -50 to get -10


f%28-5%29=-7 Add -10 and 3 to get -7


So when x=-5, we have y=-7


So our 1st point is (-5,-7)


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


f%28x%29=-2x%5E2-8x%2B3 Start with the given function


f%28-4%29=-2%28-4%29%5E2-8%28-4%29%2B3 Plug in x=-4


f%28-4%29=-2%2A16-8%2A-4%2B3 Raise -4 to the 2nd power to get 16


f%28-4%29=-32-8%2A-4%2B3 Multiply -2 and 16 to get -32


f%28-4%29=-32--32%2B3 Multiply 8 and -4 to get -32


f%28-4%29=0%2B3 Subtract -32 from -32 to get 0


f%28-4%29=3 Add 0 and 3 to get 3


So when x=-4, we have y=3


So our 2nd point is (-4,3)


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


f%28x%29=-2x%5E2-8x%2B3 Start with the given function


f%28-3%29=-2%28-3%29%5E2-8%28-3%29%2B3 Plug in x=-3


f%28-3%29=-2%2A9-8%2A-3%2B3 Raise -3 to the 2nd power to get 9


f%28-3%29=-18-8%2A-3%2B3 Multiply -2 and 9 to get -18


f%28-3%29=-18--24%2B3 Multiply 8 and -3 to get -24


f%28-3%29=6%2B3 Subtract -24 from -18 to get 6


f%28-3%29=9 Add 6 and 3 to get 9


So when x=-3, we have y=9


So our 3rd point is (-3,9)


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


f%28x%29=-2x%5E2-8x%2B3 Start with the given function


f%28-2%29=-2%28-2%29%5E2-8%28-2%29%2B3 Plug in x=-2


f%28-2%29=-2%2A4-8%2A-2%2B3 Raise -2 to the 2nd power to get 4


f%28-2%29=-8-8%2A-2%2B3 Multiply -2 and 4 to get -8


f%28-2%29=-8--16%2B3 Multiply 8 and -2 to get -16


f%28-2%29=8%2B3 Subtract -16 from -8 to get 8


f%28-2%29=11 Add 8 and 3 to get 11


So when x=-2, we have y=11


So our 4th point is (-2,11)


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


f%28x%29=-2x%5E2-8x%2B3 Start with the given function


f%28-1%29=-2%28-1%29%5E2-8%28-1%29%2B3 Plug in x=-1


f%28-1%29=-2%2A1-8%2A-1%2B3 Raise -1 to the 2nd power to get 1


f%28-1%29=-2-8%2A-1%2B3 Multiply -2 and 1 to get -2


f%28-1%29=-2--8%2B3 Multiply 8 and -1 to get -8


f%28-1%29=6%2B3 Subtract -8 from -2 to get 6


f%28-1%29=9 Add 6 and 3 to get 9


So when x=-1, we have y=9


So our 5th point is (-1,9)


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


f%28x%29=-2x%5E2-8x%2B3 Start with the given function


f%280%29=-2%280%29%5E2-8%280%29%2B3 Plug in x=0


f%280%29=-2%2A0-8%2A0%2B3 Raise 0 to the 2nd power to get 0


f%280%29=0-8%2A0%2B3 Multiply -2 and 0 to get 0


f%280%29=0-0%2B3 Multiply 8 and 0 to get 0


f%280%29=0%2B3 Subtract 0 from 0 to get 0


f%280%29=3 Add 0 and 3 to get 3


So when x=0, we have y=3


So our 6th point is (0,3)


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


f%28x%29=-2x%5E2-8x%2B3 Start with the given function


f%281%29=-2%281%29%5E2-8%281%29%2B3 Plug in x=1


f%281%29=-2%2A1-8%2A1%2B3 Raise 1 to the 2nd power to get 1


f%281%29=-2-8%2A1%2B3 Multiply -2 and 1 to get -2


f%281%29=-2-8%2B3 Multiply 8 and 1 to get 8


f%281%29=-10%2B3 Subtract 8 from -2 to get -10


f%281%29=-7 Add -10 and 3 to get -7


So when x=1, we have y=-7


So our 7th point is (1,-7)


Now lets make a table of the values we have calculated 



 xy



 -5-7
 

 -43
 

 -39
 

 -211
 

 -19
 

 03
 

 1-7
Now plot the points



Now connect the points to graph y=-2x%5E2-8x%2B3 (note: the more points you plot, the easier it is to draw the graph)