SOLUTION: Use a table of solutions to graph the quadratic equation y = x^2 + 1

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Question 114165: Use a table of solutions to graph the quadratic equation y = x^2 + 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's find values of y when x is from -3 to 3
note: remember, f(x) is the same as y




Let's evaluate f%28-3%29


f%28x%29=x%5E2%2B1 Start with the given function.


f%28-3%29=%28-3%29%5E2%2B1 Plug in x=-3. In other words, replace each x with -3.


f%28-3%29=%289%29%2B1 Evaluate %28-3%29%5E2 to get 9.


f%28-3%29=10 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%28-2%29


f%28x%29=x%5E2%2B1 Start with the given function.


f%28-2%29=%28-2%29%5E2%2B1 Plug in x=-2. In other words, replace each x with -2.


f%28-2%29=%284%29%2B1 Evaluate %28-2%29%5E2 to get 4.


f%28-2%29=5 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%28-1%29


f%28x%29=x%5E2%2B1 Start with the given function.


f%28-1%29=%28-1%29%5E2%2B1 Plug in x=-1. In other words, replace each x with -1.


f%28-1%29=%281%29%2B1 Evaluate %28-1%29%5E2 to get 1.


f%28-1%29=2 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%280%29


f%28x%29=x%5E2%2B1 Start with the given function.


f%280%29=%280%29%5E2%2B1 Plug in x=0. In other words, replace each x with 0.


f%280%29=%280%29%2B1 Evaluate %280%29%5E2 to get 0.


f%280%29=1 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%281%29


f%28x%29=x%5E2%2B1 Start with the given function.


f%281%29=%281%29%5E2%2B1 Plug in x=1. In other words, replace each x with 1.


f%281%29=%281%29%2B1 Evaluate %281%29%5E2 to get 1.


f%281%29=2 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%282%29


f%28x%29=x%5E2%2B1 Start with the given function.


f%282%29=%282%29%5E2%2B1 Plug in x=2. In other words, replace each x with 2.


f%282%29=%284%29%2B1 Evaluate %282%29%5E2 to get 4.


f%282%29=5 Now combine like terms


-----------Now let's evaluate another value---------


Let's evaluate f%283%29


f%28x%29=x%5E2%2B1 Start with the given function.


f%283%29=%283%29%5E2%2B1 Plug in x=3. In other words, replace each x with 3.


f%283%29=%289%29%2B1 Evaluate %283%29%5E2 to get 9.


f%283%29=10 Now combine like terms



Now lets make a table of the values we have calculated 



 xy



 -310
 

 -25
 

 -12
 

 01
 

 12
 

 25
 

 310
Now plot the points



Now connect the points to graph y=x%5E2%2B1 (note: the more points you plot, the easier it is to draw the graph)