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On the graph of y = (x + 2)^2 - 10, how many points are there whose coordinates are both negative integers?

 Oct 13, 2022
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On the graph of y = (x + 2)^2 - 10, how many points are there whose coordinates are both negative integers?     


          y  =  (x + 2)2 – 10     

 

          Considering only integers, it's obvious that when x < –6     

          then y goes positive, so with so few let's just try them all.     

 

          when x = –1,  y  =    –9     

          when x = –2,  y  =  –10     

          when x = –3,  y  =    –9     

          when x = –4,  y  =    –6     

          when x = –5,  y  =    –1        so there are five such points.     

.     

 Aug 28, 2025

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