Question

graph this function:
y = |x| - 4
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 \( y = |x| - 4 \), we can rewrite it as \( y = |x - 0| - 4 \). So, the vertex \((h, k)\) is \((0, -4)\).

Step2: Plot the vertex

On the given coordinate plane, the x - coordinate of the vertex is 0 and the y - coordinate is - 4. So we plot the point \((0, - 4)\) as the vertex.

Step3: Find other points to graph the function

For \( x>0 \), the function \( y = |x| - 4 \) becomes \( y=x - 4 \). Let's take \( x = 4 \), then \( y=4 - 4=0 \), so the point \((4,0)\) is on the graph. For \( x<0 \), the function \( y = |x| - 4 \) becomes \( y=-x - 4 \). Let's take \( x=-4 \), then \( y = -(-4)-4=4 - 4 = 0 \), so the point \((-4,0)\) is on the graph. We can also take \( x = 2 \), then \( y=2 - 4=-2 \), so the point \((2,-2)\) is on the graph. For \( x=-2 \), \( y=-(-2)-4=2 - 4=-2 \), so the point \((-2,-2)\) is on the graph. After plotting the vertex and these additional points, we can draw the V - shaped graph of the absolute value function.

Answer:

The vertex of the function \( y = |x| - 4 \) is at the point \((0, - 4)\), and the graph is a V - shaped graph opening upwards with additional points like \((4,0)\), \((-4,0)\), \((2,-2)\), \((-2,-2)\) etc. (To complete the graph, plot the vertex \((0, - 4)\) first and then use the symmetry of the absolute value function to plot other points and draw the graph.)