The Question does not have any instructions as regards the action to be taken w.r.t f(x)= 4x² + 12 x³ . However, this can be discussed as follows:

The factorization is 4x²(1+3x)

The graph of the function would have x-intercepts at x=0 and x= -1/3.

The graph would pass through the origin. Its y- intercept would be y=0

The graph would rise to the right and fall to the left, because it is a polynomial function of odd degree with positive leading coefficient.

As the function has a double root at x=0, the graph would touch x-axis at x=0 and turn around before falling to the left through x= -1/3

The graph would be as follows:

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