To be able to graph y=x^3+3x^2-6x, let's first determine what time of equation is it.
The expression appears to be a cubic equation.
For a cubic equation, you must be familiarized that its standard graph appears to be like this:
Let's now plot the graph of the equation.
Step 1: Identify some points of the graph.
To be able to get the coordinates of some points that pass through the graph, we think of a value of x and substitute it to the equation to get the y.
We get,
x Computations y Coordinates
-4 = (-4)^3+3(-4)^2-6(-4) 8 (-4,8)
-1 = (-1)^3+3(-1)^2-6(-1) 8 (-1,8)
0 = (0)^3+3(0)^2-6(0) 0 (0,0)
1 = (1)^3+3(1)^2-6(1) -2 (1,-2)
2 = (2)^3+3(2)^2-6(2) 8 (2,8)
After testing different samples of x and getting its respective y coordinate, we plot the graph of the equation.