SOLUTION: How do you graph the equation: {{{x^2-8x+7}}}?

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Question 316651: How do you graph the equation: x%5E2-8x%2B7?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Table of Contents:


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In order to graph y=x%5E2-8x%2B7, we need to plot some points.


Let's find y when x=0
(Note: you can start with any x-value):


y=x%5E2-8x%2B7 Start with the given equation.


y=%280%29%5E2-8%280%29%2B7 Plug in x=0.


y=1%280%29-8%280%29%2B7 Square 0 to get 0.


y=0-8%280%29%2B7 Multiply 1 and 0 to get 0.


y=0%2B0%2B7 Multiply -8 and 0 to get 0.


y=7 Combine like terms.


So when x=0, then y=7.


So we have the point .


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Let's find y when x=1:


y=x%5E2-8x%2B7 Start with the given equation.


y=%281%29%5E2-8%281%29%2B7 Plug in x=1.


y=1%281%29-8%281%29%2B7 Square 1 to get 1.


y=1-8%281%29%2B7 Multiply 1 and 1 to get 1.


y=1-8%2B7 Multiply -8 and 1 to get -8.


y=0 Combine like terms.


So when x=1, then y=0.


So we have the point .


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Let's find y when x=2:


y=x%5E2-8x%2B7 Start with the given equation.


y=%282%29%5E2-8%282%29%2B7 Plug in x=2.


y=1%284%29-8%282%29%2B7 Square 2 to get 4.


y=4-8%282%29%2B7 Multiply 1 and 4 to get 4.


y=4-16%2B7 Multiply -8 and 2 to get -16.


y=-5 Combine like terms.


So when x=2, then y=-5.


So we have the point .


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Let's find y when x=3:


y=x%5E2-8x%2B7 Start with the given equation.


y=%283%29%5E2-8%283%29%2B7 Plug in x=3.


y=1%289%29-8%283%29%2B7 Square 3 to get 9.


y=9-8%283%29%2B7 Multiply 1 and 9 to get 9.


y=9-24%2B7 Multiply -8 and 3 to get -24.


y=-8 Combine like terms.


So when x=3, then y=-8.


So we have the point .


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


Let's find y when x=4:


y=x%5E2-8x%2B7 Start with the given equation.


y=%284%29%5E2-8%284%29%2B7 Plug in x=4.


y=1%2816%29-8%284%29%2B7 Square 4 to get 16.


y=16-8%284%29%2B7 Multiply 1 and 16 to get 16.


y=16-32%2B7 Multiply -8 and 4 to get -32.


y=-9 Combine like terms.


So when x=4, then y=-9.


So we have the point .


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Let's find y when x=5:


y=x%5E2-8x%2B7 Start with the given equation.


y=%285%29%5E2-8%285%29%2B7 Plug in x=5.


y=1%2825%29-8%285%29%2B7 Square 5 to get 25.


y=25-8%285%29%2B7 Multiply 1 and 25 to get 25.


y=25-40%2B7 Multiply -8 and 5 to get -40.


y=-8 Combine like terms.


So when x=5, then y=-8.


So we have the point .


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Let's find y when x=6:


y=x%5E2-8x%2B7 Start with the given equation.


y=%286%29%5E2-8%286%29%2B7 Plug in x=6.


y=1%2836%29-8%286%29%2B7 Square 6 to get 36.


y=36-8%286%29%2B7 Multiply 1 and 36 to get 36.


y=36-48%2B7 Multiply -8 and 6 to get -48.


y=-5 Combine like terms.


So when x=6, then y=-5.


So we have the point .


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Let's find y when x=7:


y=x%5E2-8x%2B7 Start with the given equation.


y=%287%29%5E2-8%287%29%2B7 Plug in x=7.


y=1%2849%29-8%287%29%2B7 Square 7 to get 49.


y=49-8%287%29%2B7 Multiply 1 and 49 to get 49.


y=49-56%2B7 Multiply -8 and 7 to get -56.


y=0 Combine like terms.


So when x=7, then y=0.


So we have the point .


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Let's find y when x=8:


y=x%5E2-8x%2B7 Start with the given equation.


y=%288%29%5E2-8%288%29%2B7 Plug in x=8.


y=1%2864%29-8%288%29%2B7 Square 8 to get 64.


y=64-8%288%29%2B7 Multiply 1 and 64 to get 64.


y=64-64%2B7 Multiply -8 and 8 to get -64.


y=7 Combine like terms.


So when x=8, then y=7.


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
07


10


2-5


3-8


4-9


5-8


6-5


70


87

Now let's plot the points:







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Graph:


Now draw a curve through all of the points to graph y=x%5E2-8x%2B7:


Graph of y=x%5E2-8x%2B7