SOLUTION: how do you use a table of values to graph y=x^2-2x-8

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Question 131611: how do you use a table of values to graph
y=x^2-2x-8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph f%28x%29=1x%5E2-2x-8, 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=1x%5E2-2x-8 Start with the given function


f%28-3%29=1%28-3%29%5E2-2%28-3%29-8 Plug in x=-3


f%28-3%29=1%2A9-2%2A-3-8 Raise -3 to the 2nd power to get 9


f%28-3%29=9-2%2A-3-8 Multiply 1 and 9 to get 9


f%28-3%29=9--6-8 Multiply 2 and -3 to get -6


f%28-3%29=15-8 Subtract -6 from 9 to get 15


f%28-3%29=7 Subtract 8 from 15 to get 7


So when x=-3, we have y=7


So our 1st point is (-3,7)


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


f%28x%29=1x%5E2-2x-8 Start with the given function


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


f%28-2%29=1%2A4-2%2A-2-8 Raise -2 to the 2nd power to get 4


f%28-2%29=4-2%2A-2-8 Multiply 1 and 4 to get 4


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


f%28-2%29=8-8 Subtract -4 from 4 to get 8


f%28-2%29=0 Subtract 8 from 8 to get 0


So when x=-2, we have y=0


So our 2nd point is (-2,0)


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


f%28x%29=1x%5E2-2x-8 Start with the given function


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


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


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


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


f%28-1%29=3-8 Subtract -2 from 1 to get 3


f%28-1%29=-5 Subtract 8 from 3 to get -5


So when x=-1, we have y=-5


So our 3rd point is (-1,-5)


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


f%28x%29=1x%5E2-2x-8 Start with the given function


f%280%29=1%280%29%5E2-2%280%29-8 Plug in x=0


f%280%29=1%2A0-2%2A0-8 Raise 0 to the 2nd power to get 0


f%280%29=0-2%2A0-8 Multiply 1 and 0 to get 0


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


f%280%29=0-8 Subtract 0 from 0 to get 0


f%280%29=-8 Subtract 8 from 0 to get -8


So when x=0, we have y=-8


So our 4th point is (0,-8)


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


f%28x%29=1x%5E2-2x-8 Start with the given function


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


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


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


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


f%281%29=-1-8 Subtract 2 from 1 to get -1


f%281%29=-9 Subtract 8 from -1 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=1x%5E2-2x-8 Start with the given function


f%282%29=1%282%29%5E2-2%282%29-8 Plug in x=2


f%282%29=1%2A4-2%2A2-8 Raise 2 to the 2nd power to get 4


f%282%29=4-2%2A2-8 Multiply 1 and 4 to get 4


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


f%282%29=0-8 Subtract 4 from 4 to get 0


f%282%29=-8 Subtract 8 from 0 to get -8


So when x=2, we have y=-8


So our 6th point is (2,-8)


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


f%28x%29=1x%5E2-2x-8 Start with the given function


f%283%29=1%283%29%5E2-2%283%29-8 Plug in x=3


f%283%29=1%2A9-2%2A3-8 Raise 3 to the 2nd power to get 9


f%283%29=9-2%2A3-8 Multiply 1 and 9 to get 9


f%283%29=9-6-8 Multiply 2 and 3 to get 6


f%283%29=3-8 Subtract 6 from 9 to get 3


f%283%29=-5 Subtract 8 from 3 to get -5


So when x=3, we have y=-5


So our 7th point is (3,-5)


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


f%28x%29=1x%5E2-2x-8 Start with the given function


f%284%29=1%284%29%5E2-2%284%29-8 Plug in x=4


f%284%29=1%2A16-2%2A4-8 Raise 4 to the 2nd power to get 16


f%284%29=16-2%2A4-8 Multiply 1 and 16 to get 16


f%284%29=16-8-8 Multiply 2 and 4 to get 8


f%284%29=8-8 Subtract 8 from 16 to get 8


f%284%29=0 Subtract 8 from 8 to get 0


So when x=4, we have y=0


So our 8th point is (4,0)


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


f%28x%29=1x%5E2-2x-8 Start with the given function


f%285%29=1%285%29%5E2-2%285%29-8 Plug in x=5


f%285%29=1%2A25-2%2A5-8 Raise 5 to the 2nd power to get 25


f%285%29=25-2%2A5-8 Multiply 1 and 25 to get 25


f%285%29=25-10-8 Multiply 2 and 5 to get 10


f%285%29=15-8 Subtract 10 from 25 to get 15


f%285%29=7 Subtract 8 from 15 to get 7


So when x=5, we have y=7


So our 9th point is (5,7)


Now lets make a table of the values we have calculated 



 xy



 -37
 

 -20
 

 -1-5
 

 0-8
 

 1-9
 

 2-8
 

 3-5
 

 40
 

 57
Now plot the points



Now connect the points to graph y=1x%5E2-2x-8 (note: the more points you plot, the easier it is to draw the graph)