What is the range of #y = 3x^2 - 7#?
Since your function is a quadratic and the quadratic coefficient is positively-signed, it has a single minimum value, and extends upwards towards
Therefore, when you've found the smallest possible y value, that's your lower bound.
Since the second degree term is not horizontally shifted (that is,
So, your range is:
#color(blue)([-7", " oo ))#
Another way is to see that
Hence the range is