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. In other words, they are points on the graph where the curve touches zero. 
, 
, and 
. Therefore, you need to look for a function that will equal zero at these x values. 
will equal zero when 
, because the factor of 
will equal zero. The matching factors for the other two zeroes, 
and 
, are 
and 
, respectively. 
has all of these factors, but it is not the answer because it has an additional zero that would be visible on the graph. Notice it has a factor of 
, which results in a zero at 
. This additional zero that isn't present in the graph indicates that this cannot be matching function. 
is the answer because it has all of the required factors and, as a result, the required zeroes, while not having additional zeroes. Notice that the constant coefficient of negative 2 does not affect where the zeroes are. 
where 
). 
, 
, and at a value in between 1.5 and 2.
(which will make 
when 
), a factor of 
to make 
when 
, and a factor which will make 
when 
is at a value between 1.5 and 2.
and an 
factor. Additionally, the third factor, 
, will result in 
when 
, which fits the image. It also does not have any extra zeroes that would contradict the graph.
Nicole
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College of St Benedict, Bachelor in Arts, Economics. University of South Florida-Main Campus, Master of Arts, Economics.
Erin
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Messiah College, Bachelor of Science, Health Sciences, General. Messiah College, Master of Science, Occupational Therapy.
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