Answer:
f(x) = x (x – a)(x – b)^2
Step-by-step explanation:
The graphed function is of 4th degree. There only one answer choice that is 4th-degree—the one listed above.
You know the degree is even because both end behaviours have the same sign.
You know there is one double root and two single roots because of the number of zero crossings and the zero "touch". That is, the total number of roots is 4.
These observations are sufficient to identify the correct answer choice.
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You can also observe that one of the single roots is x=0, so x (to the first power) will be a factor. That eliminates the 2nd and 4th choices. You know there is an even-multiplicity root at x < 0, because the graph touches, but does not cross the x-axis. That eliminates the 3rd choice.
(x-axis labelling is inconsistent, so we cannot tell the actual root values.)
