SOLUTION: List the four smallest elements of the set. (Enter your answers as a comma-separated list.) {y|y = x2 − 9, x is in integers}

Question 1152401: List the four smallest elements of the set. (Enter your answers as a comma-separated list.)
{y|y = x2 − 9, x is in integers}
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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The parabola  y = x^2 -9  has the x-intercepts  -3 and 3  (from the equation

x^2 - 9 = 0,  which is equivalent to  y^2 = 9).



So, the parabola has the symmetry line x= 0 and the minimum  y= -9  at x= 0.



Next, the parabola INCREASES as x increases x= 1, 2, 3, 4 and so on,

and the corresponding values of y are 


   -9+1^2 = -9_1 = -8;  -9+2^2 = -9+4 = -5;  -9+3^2 = -9+9 = 0;  -9+4^2 = -9+16 = 7.


By the way, when x = -1, -2, -3, -4,  you have the same values of y, by symmetry.


So, the ANSWER  to the problem is  this list of increasing values of y {-9, -8, -5, 0}.

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Solved, explained and completed.

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