Finding the range of y=x2+2x+42x2+4x+9 (and y=quadraticquadratic in general)
Finding the range of (and in general)
Answer & Explanation
The question can be easily solved by this technique:
Squares can never be less than zero so the minmum value of the function: would be 7, or Maximum value of .
This tells that miminum value of y will be .
From here you can easily tell the maximum and minimum values:
Now find the extremes of the range of the expression in the RHS of the above equation (which I believe you can; if not someone else or I myself shall try and add it) and divide them by 2 to get the required extremes(taking half since we get values for 2y and not y).