Question

How do you graph `y=-|x+2|`?

Answer 1

graph{-|x+2| [-10, 10, -5, 5]}

Explanation:

graph{x+2 [-10, 10, -5, 5]}

This is `x+2=y` . When there's an absolute value bracket, it means that the y cannot equal to anything below zero (as they turn into a positive number)

So you subsitute 0 into the y to find the roots (the x-intercepts, it's where y=0) and solve for x.

`x+2>= 0`
`x >= -2`

So now we know that the negative part of the graph ( `y<0`) must be reflected when it hits the coordinate (-2,0)

graph{|x+2| [-10, 10, -5, 5]}

This is `|x+2|` . But since the minus sign for `-|x+2|` is on the outside of the equation instead of the inside, it will affect the equation even after the absolute value brackets.

You flip your whole equation along the x-axis for your answer.