SOLUTION: Sketch the graph of f(x)= x2-3 for f(2)

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Question 150921: Sketch the graph of f(x)= x2-3 for f(2)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Table of Contents:


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Jump to Graph


In order to graph y=x%5E2-3, we need to plot some points.


Let's find y when x=-3
(Note: you can start with any x-value):


y=x%5E2-3 Start with the given equation.


y=%28-3%29%5E2-3 Plug in x=-3.


y=1%289%29-3 Square -3 to get 9.


y=9-3 Multiply 1 and 9 to get 9.


y=6 Combine like terms.


So when x=-3, then y=6.


So we have the point .


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Let's find y when x=-2:


y=x%5E2-3 Start with the given equation.


y=%28-2%29%5E2-3 Plug in x=-2.


y=1%284%29-3 Square -2 to get 4.


y=4-3 Multiply 1 and 4 to get 4.


y=1 Combine like terms.


So when x=-2, then y=1.


So we have the point .


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Let's find y when x=-1:


y=x%5E2-3 Start with the given equation.


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


y=1%281%29-3 Square -1 to get 1.


y=1-3 Multiply 1 and 1 to get 1.


y=-2 Combine like terms.


So when x=-1, then y=-2.


So we have the point .


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Let's find y when x=0:


y=x%5E2-3 Start with the given equation.


y=%280%29%5E2-3 Plug in x=0.


y=1%280%29-3 Square 0 to get 0.


y=0-3 Multiply 1 and 0 to get 0.


y=-3 Combine like terms.


So when x=0, then y=-3.


So we have the point .


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Let's find y when x=1:


y=x%5E2-3 Start with the given equation.


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


y=1%281%29-3 Square 1 to get 1.


y=1-3 Multiply 1 and 1 to get 1.


y=-2 Combine like terms.


So when x=1, then y=-2.


So we have the point .


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Let's find y when x=2:


y=x%5E2-3 Start with the given equation.


y=%282%29%5E2-3 Plug in x=2.


y=1%284%29-3 Square 2 to get 4.


y=4-3 Multiply 1 and 4 to get 4.


y=1 Combine like terms.


So when x=2, then y=1.


So we have the point .


----------------------------------------------------


Let's find y when x=3:


y=x%5E2-3 Start with the given equation.


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


y=1%289%29-3 Square 3 to get 9.


y=9-3 Multiply 1 and 9 to get 9.


y=6 Combine like terms.


So when x=3, then y=6.


So we have the point .


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Now let's make a table of the values we just found.


Table of Values:





xy
-36


-21


-1-2


0-3


1-2


21


36

Now let's plot the points:







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Graph:


Now draw a curve through all of the points to graph y=x%5E2-3:


Graph of y=x%5E2-3