graph the equation.\ny = 4|x|

Explanation:

Step 1: Identify the function type

Absolute value function with vertical stretch.

Step 2: Determine vertex and slope

Vertex at (0,0), slope ±4 for x>0 and x<0.

Step 3: Plot key points

x=-2→y=8, x=-1→y=4, x=0→y=0, x=1→y=4, x=2→y=8.

Step 4: Draw the graph

Connect points with two straight lines forming a "V" opening upwards.

Answer:

The graph is a "V" shape with vertex at the origin (0,0), opening upwards. For positive x, it follows ( y = 4x ); for negative x, it follows ( y = -4x ). Key points include (-2,8), (-1,4), (0,0), (1,4), (2,8), with straight lines connecting them on both sides of the y-axis.