Question

graph the equation.
$y = -3|x - 6|$

Explanation:

Step1: Identify Vertex

The general form of an absolute - value function is \(y = a|x - h|+k\), where \((h,k)\) is the vertex. For the function \(y=-3|x - 6|\), \(h = 6\) and \(k = 0\), so the vertex is \((6,0)\).

Step2: Determine Direction and Stretch

Since \(a=-3\), the graph opens downward (because \(a<0\)) and is vertically stretched by a factor of 3.

Step3: Find Other Points

• When \(x = 5\), \(y=-3|5 - 6|=-3|-1|=-3\). So the point is \((5,-3)\).
• When \(x = 7\), \(y=-3|7 - 6|=-3|1|=-3\). So the point is \((7,-3)\).
• When \(x = 4\), \(y=-3|4 - 6|=-3|-2|=-6\). So the point is \((4,-6)\).
• When \(x = 8\), \(y=-3|8 - 6|=-3|2|=-6\). So the point is \((8,-6)\).

Plot the vertex \((6,0)\) and the other points \((5,-3)\), \((7,-3)\), \((4,-6)\), \((8,-6)\) and draw a V - shaped graph (opening downward) through these points.

Answer:

The graph is a V - shaped graph with vertex at \((6,0)\), opening downward, passing through points like \((5, - 3)\), \((7,-3)\), \((4,-6)\), \((8,-6)\) (the actual graph is drawn by plotting these points and connecting them in a V - shape).