Answer
Please look into graph
Work Step by Step
$f(x) = (x - 1)(x + 3)^2$
Step 1.
$f(x) = x^3 + 5x^2 + 3x - 9$ is a degree 3 polynomial
End behavior as $y = x^3$ for large x
Step 2.
Y-Intercept = $f(0) = -9$
X-Intercept when $f(x) = 0$ gives $x = -3, 1$
Step 3.
Zeros of the function are $x = -3, 1$
Multiplicity of Zero -3 is 2(even) so the graph of f touches the x-axis at x = -3.
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
$f(1) = 0$, $f(-1) = -8$, $f(0) = -9$, $f(2) = 25$ , $f(2) = -3$
