As long as it is a quadratic function, it can be balanced or completely squared, and then look at the definition domain.

Example: y = ax 2+bx+c = a [x 2+bx/a+(b 2)/(4a 2)-(b 2)/(4a 2)]+C.

=a(x+b/2a)^2-a(b^2)/(4a^2)+c

If -b/2a is in the domain.

Because a (x+b/2a) 2 is equal to 0, when x is an arbitrary real number and a is greater than zero, the range of values is-a (b 2)/(4a 2)+c to positive infinity, and when a is less than zero, the range of values is negative infinity to-a (b 2)/(4a 2)+.

Given the domain, and -b/2a is in the domain, the two largest and smallest numbers in the domain are brought into it as appropriate. If -b/2a is not in the domain, bring in the largest and smallest numbers in the domain and compare the values.