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1.     Graph the function.

f(x) = -3x^3-6x^2+3x+6

Name any x-intercepts and y-intercepts in the graph of the function.

Answer:

 Sep 27, 2019
 #1
avatar+2847 
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Y intercept is 6, its always the constant. Only time there is more than one intercept is when the graph is a circle or ellipse.

 

 

For x intercepts, that is when y is equal to 0.

 

So you set up your cubic polynomial like this:

 

-3x^3 - 6x^2 + 3x + 6 = 0

 

Before you solve, always check if x = 1 is a solution, this will save you A LOT of time.

 

So substitute in:

 

-3 - 6 + 3 + 6 = 0

 

0=0

 

Looks like x = 1 IS a solution

 

Another thing is to check if x = -1 is a solution

 

So, 3 - 6 - 3 + 6 = 0

 

0 = 0


Looks like x = -1 IS a solution.

 

This is the standard form : ax^3 + bx^2 + cx + d = 0

 

Always check if d/a is  a solution.

 

So checking x = -2

 

24 + -24 - 6 + 6 = 0

 

0 = 0

 

 

 

So we know that the x intercepts are 1, -1, and -2.

 Sep 28, 2019

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