SOLUTION: Make a table of at least 7 ordered pairs that satisfy the equation {{{y=x^2-3}}}. Then use your table to graph the function.

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Question 128612: Make a table of at least 7 ordered pairs that satisfy the equation y=x%5E2-3. Then use your table to graph the function.
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!
In order to generate ordered pairs, we need to plot evaluate some x values to get some y values to get the points.


So let's find the first point:



f%28x%29=1x%5E2-3 Start with the given function


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


f%28-5%29=1%2A25-3 Raise -5 to the 2nd power to get 25


f%28-5%29=25-3 Multiply 1 and 25 to get 25


f%28-5%29=22 Subtract 3 from 25 to get 22


So when x=-5, we have y=22


So our 1st point is (-5,22)


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


f%28x%29=1x%5E2-3 Start with the given function


f%28-4%29=1%28-4%29%5E2-3 Plug in x=-4


f%28-4%29=1%2A16-3 Raise -4 to the 2nd power to get 16


f%28-4%29=16-3 Multiply 1 and 16 to get 16


f%28-4%29=13 Subtract 3 from 16 to get 13


So when x=-4, we have y=13


So our 2nd point is (-4,13)


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


f%28x%29=1x%5E2-3 Start with the given function


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


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


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


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


So when x=-3, we have y=6


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


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


f%28x%29=1x%5E2-3 Start with the given function


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


f%28-2%29=1%2A4-3 Raise -2 to the 2nd power to get 4


f%28-2%29=4-3 Multiply 1 and 4 to get 4


f%28-2%29=1 Subtract 3 from 4 to get 1


So when x=-2, we have y=1


So our 4th point is (-2,1)


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


f%28x%29=1x%5E2-3 Start with the given function


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


f%28-1%29=1%2A1-3 Raise -1 to the 2nd power to get 1


f%28-1%29=1-3 Multiply 1 and 1 to get 1


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


So when x=-1, we have y=-2


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


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


f%28x%29=1x%5E2-3 Start with the given function


f%280%29=1%280%29%5E2-3 Plug in x=0


f%280%29=1%2A0-3 Raise 0 to the 2nd power to get 0


f%280%29=0-3 Multiply 1 and 0 to get 0


f%280%29=-3 Subtract 3 from 0 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=1x%5E2-3 Start with the given function


f%281%29=1%281%29%5E2-3 Plug in x=1


f%281%29=1%2A1-3 Raise 1 to the 2nd power to get 1


f%281%29=1-3 Multiply 1 and 1 to get 1


f%281%29=-2 Subtract 3 from 1 to get -2


So when x=1, we have y=-2


So our 7th point is (1,-2)


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


f%28x%29=1x%5E2-3 Start with the given function


f%282%29=1%282%29%5E2-3 Plug in x=2


f%282%29=1%2A4-3 Raise 2 to the 2nd power to get 4


f%282%29=4-3 Multiply 1 and 4 to get 4


f%282%29=1 Subtract 3 from 4 to get 1


So when x=2, we have y=1


So our 8th point is (2,1)


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


f%28x%29=1x%5E2-3 Start with the given function


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


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


f%283%29=9-3 Multiply 1 and 9 to get 9


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


So when x=3, we have y=6


So our 9th point is (3,6)


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


f%28x%29=1x%5E2-3 Start with the given function


f%284%29=1%284%29%5E2-3 Plug in x=4


f%284%29=1%2A16-3 Raise 4 to the 2nd power to get 16


f%284%29=16-3 Multiply 1 and 16 to get 16


f%284%29=13 Subtract 3 from 16 to get 13


So when x=4, we have y=13


So our 10th point is (4,13)


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


f%28x%29=1x%5E2-3 Start with the given function


f%285%29=1%285%29%5E2-3 Plug in x=5


f%285%29=1%2A25-3 Raise 5 to the 2nd power to get 25


f%285%29=25-3 Multiply 1 and 25 to get 25


f%285%29=22 Subtract 3 from 25 to get 22


So when x=5, we have y=22


So our 11th point is (5,22)


Now lets make a table of the values we have calculated 



 xy



 -522
 

 -413
 

 -36
 

 -21
 

 -1-2
 

 0-3
 

 1-2
 

 21
 

 36
 

 413
 

 522

Now plot the points. Note: you need to use Firefox to see the next two graphs.



Now connect the points to graph y=1x%5E2-3 (note: the more points you plot, the easier it is to draw the graph)