Hi Juriemagic :)
y is the graph of the first derivate, not of the original function so you can ignore all the derivative notation
Graph y=f′(x)=mx2+nx+k goes through the points P(-1/3;0), Q(1;0) and R(0;1). Detremine the values of m, n and k.
becomes
Graph y=mx2+nx+k goes through the points P(-1/3;0), Q(1;0) and R(0;1). Detremine the values of m, n and k.
There are at most 2 roots becasue the highest power of x is 2
P and Q are the roots because the y values are 0 so you have
y=t(x+13)(x−1) where t is some constant.
Now you use the 3rd point R(0,1) to find t
1=t(0+13)(0−1)1=t(13)(−1)1=t∗−13t=−3
So the function is y=−3(x+13)(x−1)
Now expand that our to find m, n and k
At the end substitute P, Q and R in to check it is correct. If not go find your, or mine, error.