Answer
See graph
Work Step by Step
$f(x) = x(x + 2)^2$
Step 1.
$f(x) = x^3 + 4x^2 + 4x$ is a degree 3 polynomial
End behavior as $y = x^3$ for large x
Step 2.
Y-Intercept = $f(0) = 0$
X-Intercept when $f(x) = 0$ gives $x = 0, -2$
Step 3.
Zeros of the function are $x = 0, -2$
Multiplicity of Zero 0 is 1(odd) so the graph of f crosses the x-axis at x = 0.
Multiplicity of Zero -2 is 2(even) so the graph of f touches the x-axis at x = -2.
Step 4.
Because the polynomial function is of degree 3 (Step 1), the graph of the function will have at most 3 - 1 = 2 turning points.
Step 5.
Finding values of f(x) for some x and plotting the graph using results of step 1 to 4
$f(1) = 9$, $f(-1) = -1$, $f(2) = 32$, $f(-3) = -3$