# What is the range of #y = 3x^2 - 7#?

##### 2 Answers

Aug 16, 2016

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 ))#

Aug 16, 2016

Another way is to see that

Hence the range is