Question

incorrect 2 tries left. please try again. use the graph of the function to write its equation.

Explanation:

Step1: Identify the vertex and intercepts

The graph is a V - shaped graph, so it is an absolute - value function. The general form of an absolute - value function is \(y = a|x - h|+k\), where \((h,k)\) is the vertex of the graph. From the graph, the vertex is at \((0, - 3)\) (assuming the grid has a scale where each square is 1 unit). The x - intercepts are at \(x=-3\) and \(x = 3\) (when \(y = 0\)).

Step2: Substitute the vertex into the general form

Since the vertex \((h,k)=(0,-3)\), the equation becomes \(y=a|x - 0|+(-3)=a|x|-3\).

Step3: Find the value of \(a\)

We can use one of the x - intercepts to find \(a\). Let's use the point \((3,0)\). Substitute \(x = 3\) and \(y = 0\) into the equation \(y=a|x|-3\):
\(0=a|3|-3\)
\(0 = 3a-3\)
Add 3 to both sides: \(3a=3\)
Divide both sides by 3: \(a = 1\)

Step4: Write the final equation

Substitute \(a = 1\) and \((h,k)=(0,-3)\) into the general form of the absolute - value function. We get \(y=|x|-3\)

Answer:

\(y = |x|-3\)