Answer
a. $x=-1$ and $x=\frac{3}{2}$ (multiplicity 2)
b. See graph and explanations.
Work Step by Step
a. Based on the graph, we can identify a zero as $x=-1$. Using synthetic division, we can find the quotient as $4x^2-12x+9=(2x-3)^2$, as shown in the figure. Thus the zeros are $x=-1$ and $x=\frac{3}{2}$ (multiplicity 2).
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 $y=f(0)=9$. 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.
