Get the Math and the Points! CC Alg I June 2017 Regents #10

June 2017 CC Alg I 10Can use the TI-83/4 to figure this one out!
The zeros are the values of x that make f(x) or y equal to zero.

Answer (1) looks like this:  only 1 zero at x = -3 which can be seen on both the graph and the table
Aug 2017 CC Alg I 10a EqAug 2017 CC Alg I 10aAug 2017 CC Alg I 10a Graph

Answer (2) looks like this with 3 zeros but only one of them is an integer value (both the table and the graph show that (-4,0) is a point
Aug 2017 CC Alg I 10b yAug 2017 CC Alg I 10b tableAug 2017 CC Alg I 10b graph

Let’s try answer (3):

Aug 2017 CC Alg I 10c EqAug 2017 CC Alg I 10c tableAug 2017 CC Alg I 10c graph
Here we can see that on the table when x = -3 y = 0 and also when x = 0 and x = 4, y is also equal to zero.  Looking at the graph we can see that the 3 x-intercepts are integer values of -3, 0 and 4.  That’s it!

Pay close attention to the signs!! We need to look for the factors with the opposite sign to ‘zero it out’!  This can be a bit counterintuitive as when -3 is a solution then the factor is (x + 3), as -3 makes x + 3 = 0.  When 4 is a solution, the factor must be (x – 4)  rather than  (x+4) as plugging in 4 would not result in zero.

 

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