a. $x=1,\pm4$ b. See graph and explanations.
Work Step by Step
a. Based on the graph, we can identify a zero as $x=-4$. Using synthetic division, we can find the quotient as $-x^2+5x-4$, as shown in the figure. Thus the zeros are $x=1,\pm4$ b. The end behaviors of the function can be found as $x\to-\infty, y\to\infty$ and $x\to\infty, y\to -\infty$ . The maximum number of turning points is $3-1=2$, and the y-intercept can be found as $y=f(0)=-16$. With the above information, we can finish the graph as shown in the figure, where the locations and values of the maximum and minimum are not a real concern at this point.