Question

What is the equation of the absolute value function?

Answer 1

in general: y = m|x|

if we were to move this to the origin (0,0) what would we have to do to the vertex point?

Answer 2

so to move the vertex (a,b) to (0,0) ; subtract a and subtract b

(a-a , b-b) = (0,0) but you dont want to do for just the origin, but for all (x,y) points

(x-a,y-b)

therefore the parent function: y = m|x| gets shifted as well to: (y-b) = m|x-a|

Answer 3

then all thats left is to define the postive slope ....

Answer 4

or negative if it opens down .... but this opens up

Answer 5

\[y-4=m \left| x+3 \right|\]

Answer 6

m is positive