Answer
See graph and explanations.
Work Step by Step
Step 1. Use synthetic division, we can find two zeros $x=1,3$ as shown in the figure.
Step 2. We can factor the the function as $f(x)=(x-1)(x-3)(2x^2-x-15)=(x-1)(x-3)(x-3)(2x+5)=(x-1)(x-3)^2(2x+5)$
Step 3. We can identify the zeros as $x=-\frac{5}{2}$ with multiplicity 1 (graph crosses the x-axis). $x=1$ with multiplicity 1 (graph crosses the x-axis). and $x=3$ with multiplicity 2 (graph touches the x-axis and turns around).
Step 4. The y-intercept $f(0)=-45$
Step 5. The lead term is $2x^4$ and the end behavior is rise to the left and rise to the right.
Step 6. Use test points as necessary to graph the function as shown in the figure.
