HElpppp pls its algebra

Question

asked Dec 11, 2023 117k views

1 Answer

Medoingthings · Answer 1 · 2023-12-18T04:14:12+0000

Answer:

y=3|x+1|+2

Explanation:

Parent absolute value function:

f(x)=|x|

Graph of the parent absolute function:

From inspection of the given graph, the graph has been vertically stretched as the slope of the left and right sides is no longer -1 and 1.

Each time the x-value increases (or decreases) by 1 unit from the vertex, the y-value increases by 3 units.

Therefore, the scale factor of the vertical stretch is 3:

$\implies 3f(x)=3|x|$

The vertex of the parent function is at the origin (0, 0).

From inspection of the given graph, the vertex is at (-1, 2).

Therefore the parent function has been translated 1 unit left and 2 units up:

$\implies 3f(x+1)+2=3|x+1|+2$

Therefore, the absolute value equation for the given graph is:

y=3|x+1|+2