Question

HElpppp pls its algebra

Answer 1

`y=3|x+1|+2`

Explanation:

Parent absolute value function:

`f(x)=|x|`

Graph of the parent absolute function:

• Line |y| = -x where x ≤ 0
• Line |y| = x where x ≥ 0
• Vertex at (0, 0)

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`