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.
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
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.