Question

graph this function:
y = |x| - 5
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 \( y = |x| - 5 \), we can rewrite it as \( y = |x - 0| + (-5) \). So, the vertex \((h, k)\) is \((0, -5)\).

Step2: Plot the vertex

On the given coordinate plane, find the point where \( x = 0 \) and \( y = -5 \). This is the vertex of the absolute - value graph.

Step3: Find other points to draw the graph

We can use the property of the absolute - value function. When \( x = 5 \), \( y=|5|-5 = 5 - 5=0 \). When \( x=-5 \), \( y = |-5|-5=5 - 5 = 0 \). We can also take \( x = 1 \), then \( y=|1|-5=-4 \); when \( x=-1 \), \( y = |-1|-5=-4 \). After plotting the vertex \((0, - 5)\) and other points like \((5,0)\), \((-5,0)\), \((1, - 4)\), \((-1, - 4)\) etc., we can draw two rays (since the absolute - value function has a "V - shape") with the vertex at \((0, - 5)\) and passing through the other calculated points.

Answer:

The vertex of the graph of \( y = |x|-5 \) is at the point \((0, - 5)\), and the graph is a "V - shaped" graph with the vertex at \((0, - 5)\) and passing through points like \((5,0)\), \((-5,0)\) etc. (To plot the graph, first plot the vertex \((0, - 5)\) and then use the symmetry of the absolute - value function to plot other points and draw the two arms of the "V").