Question

y = |x| - 6
click to plot the vertex first.

Explanation:

Step1: Identify the vertex form of absolute value function

The general form of an absolute value function is \( y = |x - h| + k \), where \((h, k)\) is the vertex. For the function \( y = |x| - 6 \), we can rewrite it as \( y = |x - 0| + (-6) \). So, the vertex \((h, k)\) is \((0, -6)\).

Step2: Plot the vertex

On the given coordinate grid, find the point where \( x = 0 \) and \( y = -6 \). This point is on the y - axis, 6 units below the origin (since \( y=-6\)).

Step3: Find other points to plot the graph (optional for identifying the vertex)

For \( x = 0 \), \( y=|0|-6=-6\) (we already have the vertex). For \( x = 6 \), \( y = |6|-6=0\), so the point is \((6, 0)\). For \( x=-6\), \( y = |-6|-6 = 0\), so the point is \((-6, 0)\). But the first step is to plot the vertex, which is \((0, -6)\).

Answer:

The vertex of the function \( y = |x| - 6 \) is at the point \((0, -6)\) on the coordinate grid. To plot the graph, first plot the vertex \((0, -6)\), then plot other points like \((6, 0)\) and \((-6, 0)\) and draw the V - shaped graph of the absolute value function.