Question

Helpo pleasssse

On my hw I have a parabola that opens down with its vertex at (-3,-6)......
For the range would I say that yER OR y < -6 ????
I'm just confused from the negative numbers

Answer 1

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

Step-by-step 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.