Question

write a piecewise - equation for the graph.
submit question
y =

Explanation:

Step1: Identify the vertex

The vertex of the absolute - value function is at the point \((- 3,0)\). The general form of an absolute - value function is \(y=a|x - h|+k\), where \((h,k)\) is the vertex of the graph. Here, \(h=-3\) and \(k = 0\), so the function is of the form \(y=a|x+3|\).

Step2: Find the value of \(a\)

We can use another point on the graph. Let's use the point \((-1,- 2)\). Substitute \(x=-1\) and \(y = - 2\) into \(y=a|x + 3|\). We get \(-2=a|-1 + 3|\), which simplifies to \(-2=a|2|\), or \(-2 = 2a\). Solving for \(a\), we divide both sides by 2: \(a=-1\).

Answer:

\(y=-|x + 3|\)