Question 86475
The given equation is  y = x(squared) + 2 


==> y = {{{x^2 + 2}}} 


The given equation is a quadratic in "x".  The graph of any quadratic equation will always be a parabola. 


Hence, the graph look like this: 



{{{ graph( 400, 400, -15, 15, -15, 15, x^2 + 2) }}} 



Hence, the solution..


This can also be worked in another way... 


Let f(x) = {{{x^2 + 2}}}


Given the equation just plug in the values for x and then make the table for x and f(x). Then plot all these points on the number line along the co-ordinate axes... 


For example when x = 0,  f(x) = 2 


x = 1 , f(x) = 3 


x = 2 . f(x) = 5 


x = 3 , f(x) = 10 


And similarly for the negative values.. 


x = -1 , f(x) = 3  


x = -2 , f(x) = 5 


x = -3 , f(x) = 10 


f(x) will have the same values, since the given function is an even function..


Thus, the solution...


Regards