Given function is f(x) = x² -6x +9.
It is a quadratic function whose graph is an upward open parabola.
The zero(s) of the given function would be at x-intercepts of the graph i.e. y = 0.
It means 0 = x² -6x +9
We can solve this quadratic equation using factorization as follows:-
0 = x² -6x +9
0 = x² -3x -3x +9
0 = x(x-3) -3(x-3)
0 = (x-3)(x-3)
Therefore, x = 3 with multiplicity two.
Hence, option C is correct, i.e. The graph of the function touches the x-axis at x = 3.
