Question

Helpo pleasssse

Answer 1

Answer: The range is  $\{y \in \mathbb{R}\ | \ y \le -6\}$

Explanation:

The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.

The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write $y \le -6$ to describe all the possible y values.

Therefore, the range is $\{y \in \mathbb{R}\ | \ y \le -6\}$

This translates to "y is a real number such that y is -6 or smaller".

So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.

See below for a visual example of what's going on.