From the figure we see that -3 is a root, 2 is a double root, and the y-intercept is (0,10).
So the cubic polynomial has the form for some constant .
See if you can find .
Hello, hejmh!
The general cubic function is: .
. . Its derivative is: .
We need to determine the four coefficients: .
We know five facts about the function:
. .
Set up a system of equations and solve.
Edit: Ah, I see that DrSteve has a nicer form of the cubic.
Because, as Dr. Steve said, x= 2 is a double root- the x-axis is tangent to the graph at x= 2.
Another way of seeing the same thing- moving from one side of 2 to the other, say from x= 1.9 to x= 2.1, changes the sign of x- 2. x- 2 must be to an even power since y does not change sign.
NO, it isn't. , not 0.2- You see in the figure f(0)=10 but in this solution f(0)=0
According to your graph may or may not be . It turns out that it is not. If you combine my post above with HallsofIvy's you will see that
.
The derivative of this function is not 0 at .
Soroban's method should work if you just leave out the condition . You will get a system of 3 equations in 3 unknowns which should have a unique solution (I'm pretty sure that the 3 equations in 2 unknowns you have above is inconsistent). You'll probably want to do Gauss-Jordan Reduction to solve this. It's quite a bit more work than the original solution I posted.