SOLUTION: Graph the polynomial function: f(x)=x^3+4x^2+x-6 Thank you for your time and effort, it is greatly appreciated

Algebra ->  Graphs -> SOLUTION: Graph the polynomial function: f(x)=x^3+4x^2+x-6 Thank you for your time and effort, it is greatly appreciated      Log On


   

Question 148855: Graph the polynomial function:
f(x)=x^3+4x^2+x-6
Thank you for your time and effort, it is greatly appreciated
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%5E3%2B4x%5E2%2Bx-6, we need to plot some points.


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


y=x%5E3%2B4x%5E2%2Bx-6 Start with the given equation.


y=%28-3%29%5E3%2B4%28-3%29%5E2%2B-3-6 Plug in x=-3.


y=1%28-27%29%2B4%28-3%29%5E2-3-6 Cube -3 to get -27.


y=1%28-27%29%2B4%289%29-3-6 Square -3 to get 9.


y=-27%2B4%289%29-3-6 Multiply 1 and -27 to get -27.


y=-27%2B36-3-6 Multiply 4 and 9 to get 36.


y=0 Combine like terms.


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


So we have the point .


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Let's find y when x=-2:


y=x%5E3%2B4x%5E2%2Bx-6 Start with the given equation.


y=%28-2%29%5E3%2B4%28-2%29%5E2%2B-2-6 Plug in x=-2.


y=1%28-8%29%2B4%28-2%29%5E2-2-6 Cube -2 to get -8.


y=1%28-8%29%2B4%284%29-2-6 Square -2 to get 4.


y=-8%2B4%284%29-2-6 Multiply 1 and -8 to get -8.


y=-8%2B16-2-6 Multiply 4 and 4 to get 16.


y=0 Combine like terms.


So when x=-2, then y=0.


So we have the point .


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Let's find y when x=-1:


y=x%5E3%2B4x%5E2%2Bx-6 Start with the given equation.


y=%28-1%29%5E3%2B4%28-1%29%5E2%2B-1-6 Plug in x=-1.


y=1%28-1%29%2B4%28-1%29%5E2-1-6 Cube -1 to get -1.


y=1%28-1%29%2B4%281%29-1-6 Square -1 to get 1.


y=-1%2B4%281%29-1-6 Multiply 1 and -1 to get -1.


y=-1%2B4-1-6 Multiply 4 and 1 to get 4.


y=-4 Combine like terms.


So when x=-1, then y=-4.


So we have the point .


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Let's find y when x=0:


y=x%5E3%2B4x%5E2%2Bx-6 Start with the given equation.


y=%280%29%5E3%2B4%280%29%5E2%2B0-6 Plug in x=0.


y=1%280%29%2B4%280%29%5E2%2B0-6 Cube 0 to get 0.


y=1%280%29%2B4%280%29%2B0-6 Square 0 to get 0.


y=0%2B4%280%29%2B0-6 Multiply 1 and 0 to get 0.


y=0%2B0%2B0-6 Multiply 4 and 0 to get 0.


y=-6 Combine like terms.


So when x=0, then y=-6.


So we have the point .


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Let's find y when x=1:


y=x%5E3%2B4x%5E2%2Bx-6 Start with the given equation.


y=%281%29%5E3%2B4%281%29%5E2%2B1-6 Plug in x=1.


y=1%281%29%2B4%281%29%5E2%2B1-6 Cube 1 to get 1.


y=1%281%29%2B4%281%29%2B1-6 Square 1 to get 1.


y=1%2B4%281%29%2B1-6 Multiply 1 and 1 to get 1.


y=1%2B4%2B1-6 Multiply 4 and 1 to get 4.


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%5E3%2B4x%5E2%2Bx-6 Start with the given equation.


y=%282%29%5E3%2B4%282%29%5E2%2B2-6 Plug in x=2.


y=1%288%29%2B4%282%29%5E2%2B2-6 Cube 2 to get 8.


y=1%288%29%2B4%284%29%2B2-6 Square 2 to get 4.


y=8%2B4%284%29%2B2-6 Multiply 1 and 8 to get 8.


y=8%2B16%2B2-6 Multiply 4 and 4 to get 16.


y=20 Combine like terms.


So when x=2, then y=20.


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
-30


-20


-1-4


0-6


10


220

Now let's plot the points:







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Graph:


Now draw a curve through all of the points to graph y=x%5E3%2B4x%5E2%2Bx-6:


Graph of y=x%5E3%2B4x%5E2%2Bx-6