graph the equation.\n$y = 2|x| - 3$

Explanation:

Step1: Find the vertex

For the absolute - value function (y = a|x - h|+k), the vertex is ((h,k)). For (y = 2|x|-3), (h = 0) and (k=-3), so the vertex is ((0,-3)).

Step2: Find points for (x\geq0)

When (x = 0), (y=2|0|-3=-3). When (x = 1), (y=2|1|-3=-1). When (x = 2), (y=2|2|-3 = 1). When (x=3), (y=2|3|-3=3).

Step3: Use symmetry

Since (y = 2|x|-3) is an even function ((y(x)=y(-x))), if ((x,y)) is on the graph, then ((-x,y)) is also on the graph. So the points ((-1,-1)), ((-2,1)), ((-3,3)) are also on the graph.

Step4: Plot the points and draw the graph

Plot the vertex ((0, - 3)) and the points ((1,-1)), ((2,1)), ((3,3)), ((-1,-1)), ((-2,1)), ((-3,3)). Then connect the points for (x\geq0) with a straight - line segment (since for (y = 2x-3) when (x\geq0)) and the points for (x<0) with a straight - line segment (since for (y=-2x - 3) when (x<0)). The graph is a "V" - shaped graph opening upwards.

Answer:

Plot the vertex ((0,-3)) and points ((\pm1,-1)), ((\pm2,1)), ((\pm3,3)) and connect them to form a "V" - shaped graph opening upwards.