Algebra 2 unit 2 question. connexus.

From the graph we can infer that our function crosses the x-axis at -2.5, 0.5, and 1.5, so those are the zeroes of the function.
Next, lets convert those decimals into fractions by adding a denominator 1 to each decimal and multiply both its numerator and denominator by a power 10 that lets us get rid of the decimal point:




Since we know that each one of those points is a zero of the function (), we can replace each value into our , and work backwards to get our binomials:



So, our first binomial is 




So, our second binomial is 




So, our next binomial is 

Now lets put all together to find the equation of our function:

And of course, we can rewrite it in a different order:


We can conclude that the equation that most likely represents the graph of the function is