# How do you find the first three iterate of the function f(x)=3x^2-3x+2 for the given initial value x_0=1/3?

If we look at the graph of the function $y = f \left(x\right)$:
$\Delta = {b}^{2} - 4 a c = 9 - 24 < 0$
Therefore $f \left(x\right) = 0$ has no (real) solution and therefore an iterative approach will fail.