Question

graph this function:
y = |x| - 4
click to plot the vertex first.

Explanation:

Step1: Identify the vertex form

The absolute - value function is in the form \(y = |x - h|-k\), where the vertex is \((h,k)\). For the function \(y=|x|-4\), we can rewrite it as \(y = |x - 0|-4\). So, \(h = 0\) and \(k=-4\).

Step2: Plot the vertex

The vertex of the function \(y = |x|-4\) is at the point \((0,-4)\) on the coordinate plane.

Step3: Find other points

For \(x = 1\), \(y=|1|-4=1 - 4=-3\), so the point is \((1,-3)\). For \(x=- 1\), \(y = |-1|-4=1 - 4=-3\), so the point is \((-1,-3)\). For \(x = 4\), \(y=|4|-4=4 - 4 = 0\), so the point is \((4,0)\). For \(x=-4\), \(y=|-4|-4=4 - 4=0\), so the point is \((-4,0)\). We can use these points to draw the V - shaped graph of the absolute - value function. First, we plot the vertex \((0,-4)\), and then we can plot the other points and draw the two rays of the absolute - value graph.

Answer:

The vertex of the function \(y = |x|-4\) is at \((0,-4)\), and the graph is a V - shaped graph with the vertex at \((0,-4)\), passing through points like \((1,-3)\), \((-1,-3)\), \((4,0)\), \((-4,0)\) etc. (To graph it, first plot the vertex \((0,-4)\) and then use the slope of \(1\) and \(- 1\) for the two branches of the absolute - value graph).