Oh yes sorry i didn't understood u yes the graph should move up and down as the points - 1 and 1 are fixing the graph's turning point. If x be very large then y will also be large as it will meet the line of graph will be a slightly straight line. If a = 0 and x= 0 then y will be zero. Am i going the right direction please check my sketch! When i add postive value of a then the graph is moving up!
Oh.. now i got the logic so do u mean that the extreme values of a should be such that the graph lies between fig1 and fig2 . Oh i am not able to upload the images because of file size but now i understood that we should take those value of a such that graph become such that the turning point touches 1 and -1 and not beyond that as the roots will then become imaginary. So is the value of a for the above case -2<a<2 ??