Answer
Please Look Into graph
Work Step by Step
$f(x) = (x + 4)^2(1 - x)$
Step 1.
$f(x) = -x^3 - 7x^2 - 8x + 16$ is a degree 3 polynomial
End behavior as $y = -x^3$ for large x
Step 2.
Y-Intercept = $f(0) = 16$
X-Intercept when $f(x) = 0$ gives $x = -4, 1$
Step 3.
Zeros of the function are $x = -4, 1$
Multiplicity of Zero -4 is 2(even) so the graph of f touches the x-axis at x = -4.
Multiplicity of Zero 1 is 1(odd) so the graph of f crosses the x-axis at x = 1.
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
$f(1) = 0$, $f(-1) = 18$, $f(0) = 16$
