graph the equation.\n$y = -3|x|$

Explanation:

Step1: Find the vertex

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

Step2: Find some points

When (x = 1), (y=-3|1|=-3). When (x=-1), (y=-3|-1|=-3). When (x = 2), (y=-3|2|=-6). When (x=-2), (y=-3|-2|=-6).

Step3: Plot the points and draw the graph

Plot the vertex ((0,0)) and the points ((1, - 3)), ((-1,-3)), ((2,-6)), ((-2,-6)). Since (a=-3<0), the graph opens downwards. Connect the points with two straight - line segments (one for (x\geq0) and one for (x<0)).

Answer:

The graph of (y =-3|x|) is a V - shaped graph opening downwards with vertex at the origin ((0,0)).