Question

What is the graph of the polynomial function

Answer 1

The roots of f(x) are {0, 3, -4}.  You've got them as {-3, 4}, which is not correct.

Draw another set of coordinate axes and place dark dots at (0,0), (3,0) and (-4,0).  These dots represent the roots (solutions) of the given polynomial.
Note that we have a repeated (double) root at x=3, which is given away by the exponent 2 of (x-3).

A basic way of sketching this graph is described as follows:

Evaluate the function (find y) for several x-values other than (0, 3 and -4):
Choose (for example) {-5, -2, -1, 1, 2, 4}

If you'll find the y-value for each of these x-values and plot the resulting points, you should see the shape of the graph.  Draw a rough graph thru these points.  If any doubt remains about what the graph looks like at particular x-values, calculate and plot more points, e. g., at {-2.5, -1.5, ...}.

If you're taking calculus, consider applying the First- and Second-Derivative tests to determine concavity, maximum, minimum, etc.