How do you graph #y=x^3-4x^2+x+6#?
Factorise to find x-intercepts
Look at the constant at the end (6) and use the factors of that number to find one of your roots. For example, if you put x = 2, that gives you 8-16+2+6 which = 0 therefore (x-2) is a factor.
You now know that the equation is a combination of (x-2) and, because it is a cubic graph, a quadratic is left over.
Now as you look at the coefficients of each term, the coeff of
To find the coeff of
Finally, you need the c which is 6 and is
Altogether this gives us
The quadratic can be factorised to give:
These three brackets give us our three x intercepts (-1, 2 and 3) and when x = 0, y = 6 which is the y intercept!!
Don't forget cubic graphs are like sideways 's'