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if you had f(x)=x3-7x+6. how would you find the x and y intercept?

JJAwsome  Apr 27, 2017
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 #1
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i know that the y-intercept is -1 but i need help with the x-intercept

JJAwsome  Apr 27, 2017
 #2
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f(x)   = x^3 - 7x  + 6

 

To find the y intercept, let x  = 0    and the y intercept   = 6

 

Note that one of the x intercepts  = 1  because

 

(1)^3  - 7(1)  +  6  =

 

1  - 7   + 6  =

 

-6  +  6  = 0

 

So  1 is a root    ( an x intercept )

 

Using synthetic division to find the remaining polynomial

 

 

1    [    1   0    - 7       6   ]

                1     1       -6

             ____________

          1    1    -6       0

 

So....the remaining polynomial is    x^2  + 1x   -  6.....set to 0 and factor

 

x^2 + 1x  -  6  = 0

 

(x + 3) ( x - 2)   = 0         set each factor to 0 and solve for x  and  x = -3  and x   = 2

 

And these are the other two x intercepts

 

Here's the graph  : https://www.desmos.com/calculator/e7h0jx35bk

 

 

cool cool cool

CPhill  Apr 27, 2017

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