SOLUTION: y=x^2+2

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Question 131616: y=x^2+2
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=1x%5E2%2B2, 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%2B2 Start with the given function


f%28-3%29=1%28-3%29%5E2%2B2 Plug in x=-3


f%28-3%29=1%2A9%2B2 Raise -3 to the 2nd power to get 9


f%28-3%29=9%2B2 Multiply 1 and 9 to get 9


f%28-3%29=11 Add 9 and 2 to get 11


So when x=-3, we have y=11


So our 1st point is (-3,11)


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


f%28x%29=1x%5E2%2B2 Start with the given function


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


f%28-2%29=1%2A4%2B2 Raise -2 to the 2nd power to get 4


f%28-2%29=4%2B2 Multiply 1 and 4 to get 4


f%28-2%29=6 Add 4 and 2 to get 6


So when x=-2, we have y=6


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


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


f%28x%29=1x%5E2%2B2 Start with the given function


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


f%28-1%29=1%2A1%2B2 Raise -1 to the 2nd power to get 1


f%28-1%29=1%2B2 Multiply 1 and 1 to get 1


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


So when x=-1, we have y=3


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


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


f%28x%29=1x%5E2%2B2 Start with the given function


f%280%29=1%280%29%5E2%2B2 Plug in x=0


f%280%29=1%2A0%2B2 Raise 0 to the 2nd power to get 0


f%280%29=0%2B2 Multiply 1 and 0 to get 0


f%280%29=2 Add 0 and 2 to get 2


So when x=0, we have y=2


So our 4th point is (0,2)


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


f%28x%29=1x%5E2%2B2 Start with the given function


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


f%281%29=1%2A1%2B2 Raise 1 to the 2nd power to get 1


f%281%29=1%2B2 Multiply 1 and 1 to get 1


f%281%29=3 Add 1 and 2 to get 3


So when x=1, we have y=3


So our 5th point is (1,3)


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


f%28x%29=1x%5E2%2B2 Start with the given function


f%282%29=1%282%29%5E2%2B2 Plug in x=2


f%282%29=1%2A4%2B2 Raise 2 to the 2nd power to get 4


f%282%29=4%2B2 Multiply 1 and 4 to get 4


f%282%29=6 Add 4 and 2 to get 6


So when x=2, we have y=6


So our 6th point is (2,6)


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


f%28x%29=1x%5E2%2B2 Start with the given function


f%283%29=1%283%29%5E2%2B2 Plug in x=3


f%283%29=1%2A9%2B2 Raise 3 to the 2nd power to get 9


f%283%29=9%2B2 Multiply 1 and 9 to get 9


f%283%29=11 Add 9 and 2 to get 11


So when x=3, we have y=11


So our 7th point is (3,11)


Now lets make a table of the values we have calculated 



 xy



 -311
 

 -26
 

 -13
 

 02
 

 13
 

 26
 

 311
Now plot the points



Now connect the points to graph y=1x%5E2%2B2 (note: the more points you plot, the easier it is to draw the graph)