Question

PLEASE HELP!

without graphing identify the vertex, axis of symmetry and transformations from the parent function:y=|x+1|+3

vertex:
axis of symmetry:
transformations:

Answer 1

Given:
Consider the given function is

To find:
The vertex , axis of symmetry, and transformations of the parent function?
Solution:
We have,


...(i)
It is an absolute function.
The vertex form of an absolute function is
...(ii)
where, a is a constant, (h,k) is vertex and x=h is axis of symmetry.
From (i) and (ii), we get

So,


Parent function of an absolute function is

Since, a=8 therefore, parent function vertically stretched by factor 8.
, so the function shifts unit right.
k=-3<0, so the function shifts 3 units down.
Therefore, the vertex is and Axis of symmetry is . The parent function Therefore, the vertex is and Axis of symmetry is . The parent function vertically stretched by factor 8, shifts unit right and 3 units down.