Question

graph this function:
y = |6x| - 8
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 \( y = a|x - h| + k \), where \((h, k)\) is the vertex. For the function \( y = |6x| - 8 \), we can rewrite \( |6x| \) as \( 6|x| \), so the function is \( y = 6|x - 0| - 8 \). Comparing with the general form, \( h = 0 \) and \( k = -8 \). So the vertex is at \((0, -8)\).

Step2: Plot the vertex

On the given coordinate plane, find the point where \( x = 0 \) and \( y = -8 \). This point is on the y - axis, 8 units below the origin.

Step3: Find other points to graph the function

For \( x>0 \), the function \( y = 6x - 8 \) (since \( |x|=x \) when \( x\geq0 \)). Let's take \( x = 1 \), then \( y=6(1)-8=-2 \). So the point \((1, -2)\) is on the graph. For \( x = 2 \), \( y = 6(2)-8 = 12 - 8=4 \), so the point \((2, 4)\) is on the graph.
For \( x<0 \), the function \( y=- 6x - 8 \) (since \( |x|=-x \) when \( x < 0 \)). Let's take \( x=-1 \), then \( y=-6(-1)-8 = 6 - 8=-2 \), so the point \((-1, -2)\) is on the graph. For \( x = - 2 \), \( y=-6(-2)-8=12 - 8 = 4 \), so the point \((-2, 4)\) is on the graph.
We can now plot these points and draw the V - shaped graph of the absolute value function with the vertex at \((0, -8)\) and passing through the other calculated points.

Answer:

The vertex of the function \( y = |6x|-8 \) is at \((0, - 8)\), and the graph is a V - shaped graph opening upwards (since \( a = 6>0 \)) with the vertex at \((0, -8)\) and passing through points like \((1, -2)\), \((-1, -2)\), \((2, 4)\), \((-2, 4)\) etc. (The main step for graphing starts with plotting the vertex \((0, -8)\)).