Question

question
use technology to find points and then graph the function ( y = -|x - 4| + 4 ), following the instructions below.
plot at least five points that fit on the axes below. click a point to delete it.
(there is a coordinate plane image here and a drag plotting points button)

Explanation:

Step1: Analyze the function

The function is \( y = -|x - 4| + 4 \). This is an absolute - value function. The general form of an absolute - value function is \( y=a|x - h|+k \), where \((h,k)\) is the vertex of the V - shaped graph. For our function, \( h = 4\) and \( k = 4\), so the vertex is \((4,4)\).

Step2: Find points by substituting x - values

• When \( x=0\):

Substitute \( x = 0\) into the function \( y=-|0 - 4|+4=-| - 4|+4=-4 + 4=0\). So the point is \((0,0)\).

• When \( x = 2\):

Substitute \( x = 2\) into the function \( y=-|2 - 4|+4=-| - 2|+4=-2 + 4 = 2\). So the point is \((2,2)\).

• When \( x=4\):

Substitute \( x = 4\) into the function \( y=-|4 - 4|+4=-|0|+4=0 + 4=4\). So the point is \((4,4)\) (the vertex).

• When \( x = 6\):

Substitute \( x = 6\) into the function \( y=-|6 - 4|+4=-|2|+4=-2 + 4=2\). So the point is \((6,2)\).

• When \( x = 8\):

Substitute \( x = 8\) into the function \( y=-|8 - 4|+4=-|4|+4=-4 + 4=0\). So the point is \((8,0)\).

To graph the function:

1. Plot the points \((0,0)\), \((2,2)\), \((4,4)\), \((6,2)\), \((8,0)\) on the coordinate plane.
2. The graph of an absolute - value function \( y = a|x - h|+k\) with \( a=- 1<0\) opens downwards. So we connect the points with a smooth V - shaped (inverted V - shaped in this case) curve.

Answer:

Some points on the graph are \((0,0)\), \((2,2)\), \((4,4)\), \((6,2)\), \((8,0)\). The graph is an inverted V - shaped graph with vertex at \((4,4)\) passing through the above - mentioned points.