Question

What inequality is graphed?

y < |x – 2| – 1

y < –|x – 2| – 1

y < |x + 2| – 1

y < –|x + 2| – 1

Answer 1

Remember that the numbers inside attached to the x value will be flipped when finding a vertex on a graph. Since the vertex of the graph is -2, -1, we can assume that the inequality will be y < |x + 2| -1 (Remember the y coordinate is always outside, the same sign and the x coordinate is on the inside with a flipped sign.) Now since it's facing downwards, we can also assume that the inequality is negative, making it y < -|x + 2| -1
I hope you understand this and not just take the answer I give you.

Answer 2

so to find the vertex the numbers flip, as in going from a neg to a pos, when plugging it back into the equation? like if i had the points (-6, 5) the equation would be
y < |x +2| +5?

Answer 3

Uhh either the -6 or +2 is not completely on the mark. It'd either be:
(-6, 5) turns to y < |x +6| +5 or
(-2, 5) turns to y < |x +2| +5

Answer 4

typo my bad but it does make alot more sense, thanks!