Answer
a. $x=-3,-2,1,3$
b. See graph and explanations.
Work Step by Step
a. Based on the graph, we can identify two zeros as $x=1,3$. Using synthetic division, we can find the quotient as $2x^2+10x+12=2(x^2+5x+6)=2(x+3)(x+2)$, as shown in the figure. Thus the zeros are $x=-3,-2,1,3$
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 of turning points is $4-1=3$, and the y-intercept can be found as $y=f(0)=36$. With the above information, we can finish the graph as shown in the figure, where the locations and values of the extrema are not a real concern at this point.
