SOLUTION: sketch the graph of f(x) + (x-3)2 + 1

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Question 150929: sketch the graph of f(x) + (x-3)2 + 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Table of Contents:

Table
Graph

In order to graph y=%28x-3%29%5E2+%2B+1, we need to plot a few points.


Let's find the y value when x=0 note: you can start at any x value.


y=%28x-3%29%5E2+%2B+1 Start with the given equation.


y=%280-3%29%5E2+%2B+1 Plug in x=0.


y=10 Simplify.


So when x=0, y=10. So we have the point (0,10).


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Let's find the y value when x=1


y=%28x-3%29%5E2+%2B+1 Start with the given equation.


y=%281-3%29%5E2+%2B+1 Plug in x=1.


y=5 Simplify.


So when x=1, y=5. So we have the point (1,5).


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Let's find the y value when x=2


y=%28x-3%29%5E2+%2B+1 Start with the given equation.


y=%282-3%29%5E2+%2B+1 Plug in x=2.


y=2 Simplify.


So when x=2, y=2. So we have the point (2,2).


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Let's find the y value when x=3


y=%28x-3%29%5E2+%2B+1 Start with the given equation.


y=%283-3%29%5E2+%2B+1 Plug in x=3.


y=1 Simplify.


So when x=3, y=1. So we have the point (3,1).


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Let's find the y value when x=4


y=%28x-3%29%5E2+%2B+1 Start with the given equation.


y=%284-3%29%5E2+%2B+1 Plug in x=4.


y=2 Simplify.


So when x=4, y=2. So we have the point (4,2).


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Let's find the y value when x=5


y=%28x-3%29%5E2+%2B+1 Start with the given equation.


y=%285-3%29%5E2+%2B+1 Plug in x=5.


y=5 Simplify.


So when x=5, y=5. So we have the point (5,5).


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Let's find the y value when x=6


y=%28x-3%29%5E2+%2B+1 Start with the given equation.


y=%286-3%29%5E2+%2B+1 Plug in x=6.


y=10 Simplify.


So when x=6, y=10. So we have the point (6,10).


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





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Table of Values:





xy
010


15


22


31


42


55


610

Now let's plot the points:







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Graph:


Now draw a curve through all of the points to graph y=%28x-3%29%5E2+%2B+1:


Graph of y=%28x-3%29%5E2+%2B+1