SOLUTION: I am trying to graph y=-x^2 -8x +9, I am not sure how to solve and graph

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Question 153191: I am trying to graph y=-x^2 -8x +9, I am not sure how to solve and graph
Answer by jim_thompson5910(28503) About Me  (Show Source):
You can put this solution on YOUR website!

Table of Contents:


Jump to Table
Jump to Graph


In order to graph y=-x%5E2-8x%2B9, we need to plot some points.


Let's find y when x=-9
(Note: you can start with any x-value):


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-9%29%5E2-8%28-9%29%2B9 Plug in x=-9.


y=-1%2881%29-8%28-9%29%2B9 Square -9 to get 81.


y=-81-8%28-9%29%2B9 Multiply -1 and 81 to get -81.


y=-81%2B72%2B9 Multiply -8 and -9 to get 72.


y=0 Combine like terms.


So when x=-9, then y=0.


So we have the point .


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Let's find y when x=-8:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-8%29%5E2-8%28-8%29%2B9 Plug in x=-8.


y=-1%2864%29-8%28-8%29%2B9 Square -8 to get 64.


y=-64-8%28-8%29%2B9 Multiply -1 and 64 to get -64.


y=-64%2B64%2B9 Multiply -8 and -8 to get 64.


y=9 Combine like terms.


So when x=-8, then y=9.


So we have the point .


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Let's find y when x=-7:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-7%29%5E2-8%28-7%29%2B9 Plug in x=-7.


y=-1%2849%29-8%28-7%29%2B9 Square -7 to get 49.


y=-49-8%28-7%29%2B9 Multiply -1 and 49 to get -49.


y=-49%2B56%2B9 Multiply -8 and -7 to get 56.


y=16 Combine like terms.


So when x=-7, then y=16.


So we have the point .


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Let's find y when x=-6:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-6%29%5E2-8%28-6%29%2B9 Plug in x=-6.


y=-1%2836%29-8%28-6%29%2B9 Square -6 to get 36.


y=-36-8%28-6%29%2B9 Multiply -1 and 36 to get -36.


y=-36%2B48%2B9 Multiply -8 and -6 to get 48.


y=21 Combine like terms.


So when x=-6, then y=21.


So we have the point .


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


Let's find y when x=-5:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-5%29%5E2-8%28-5%29%2B9 Plug in x=-5.


y=-1%2825%29-8%28-5%29%2B9 Square -5 to get 25.


y=-25-8%28-5%29%2B9 Multiply -1 and 25 to get -25.


y=-25%2B40%2B9 Multiply -8 and -5 to get 40.


y=24 Combine like terms.


So when x=-5, then y=24.


So we have the point .


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Let's find y when x=-4:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-4%29%5E2-8%28-4%29%2B9 Plug in x=-4.


y=-1%2816%29-8%28-4%29%2B9 Square -4 to get 16.


y=-16-8%28-4%29%2B9 Multiply -1 and 16 to get -16.


y=-16%2B32%2B9 Multiply -8 and -4 to get 32.


y=25 Combine like terms.


So when x=-4, then y=25.


So we have the point .


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


Let's find y when x=-3:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-3%29%5E2-8%28-3%29%2B9 Plug in x=-3.


y=-1%289%29-8%28-3%29%2B9 Square -3 to get 9.


y=-9-8%28-3%29%2B9 Multiply -1 and 9 to get -9.


y=-9%2B24%2B9 Multiply -8 and -3 to get 24.


y=24 Combine like terms.


So when x=-3, then y=24.


So we have the point .


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


Let's find y when x=-2:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-2%29%5E2-8%28-2%29%2B9 Plug in x=-2.


y=-1%284%29-8%28-2%29%2B9 Square -2 to get 4.


y=-4-8%28-2%29%2B9 Multiply -1 and 4 to get -4.


y=-4%2B16%2B9 Multiply -8 and -2 to get 16.


y=21 Combine like terms.


So when x=-2, then y=21.


So we have the point .


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


Let's find y when x=-1:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%28-1%29%5E2-8%28-1%29%2B9 Plug in x=-1.


y=-1%281%29-8%28-1%29%2B9 Square -1 to get 1.


y=-1-8%28-1%29%2B9 Multiply -1 and 1 to get -1.


y=-1%2B8%2B9 Multiply -8 and -1 to get 8.


y=16 Combine like terms.


So when x=-1, then y=16.


So we have the point .


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Let's find y when x=0:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%280%29%5E2-8%280%29%2B9 Plug in x=0.


y=-1%280%29-8%280%29%2B9 Square 0 to get 0.


y=0-8%280%29%2B9 Multiply -1 and 0 to get 0.


y=0%2B0%2B9 Multiply -8 and 0 to get 0.


y=9 Combine like terms.


So when x=0, then y=9.


So we have the point .


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


Let's find y when x=1:


y=-x%5E2-8x%2B9 Start with the given equation.


y=-%281%29%5E2-8%281%29%2B9 Plug in x=1.


y=-1%281%29-8%281%29%2B9 Square 1 to get 1.


y=-1-8%281%29%2B9 Multiply -1 and 1 to get -1.


y=-1-8%2B9 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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Now let's make a table of the values we just found.


Table of Values:





xy
-90


-89


-716


-621


-524


-425


-324


-221


-116


09


10

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%2B9:


Graph of y=-x%5E2-8x%2B9