Math  /  Algebra

QuestionGraph the equation. y=6x3y=6|x-3|

Studdy Solution

STEP 1

1. We are given the equation y=6x3 y = 6|x-3| .
2. The goal is to graph this equation on the Cartesian plane.

STEP 2

1. Understand the basic form of the absolute value function.
2. Identify the vertex of the absolute value function.
3. Determine the slope and direction of the lines forming the "V" shape.
4. Plot key points and draw the graph.

STEP 3

Understand the basic form of the absolute value function:
The basic absolute value function is y=x y = |x| , which forms a "V" shape with the vertex at the origin (0,0)(0, 0).

STEP 4

Identify the vertex of the function y=6x3 y = 6|x-3| :
The expression x3 |x-3| indicates a horizontal shift of the basic absolute value function to the right by 3 units. Therefore, the vertex of the graph is at (3,0)(3, 0).

STEP 5

Determine the slope and direction of the lines forming the "V" shape:
The coefficient 6 6 in front of the absolute value indicates a vertical stretch. The lines forming the "V" will have slopes of 6 6 and 6 -6 , starting from the vertex (3,0)(3, 0).

STEP 6

Plot key points and draw the graph:
1. Start by plotting the vertex at (3,0)(3, 0).
2. From the vertex, use the slope 6 6 to plot a point to the right. For example, moving one unit right from (3,0)(3, 0) to (4,6)(4, 6).
3. Use the slope 6-6 to plot a point to the left. For example, moving one unit left from (3,0)(3, 0) to (2,6)(2, 6).
4. Draw lines through these points to form the "V" shape.

The graph of the equation y=6x3 y = 6|x-3| is a "V" shape with the vertex at (3,0)(3, 0), opening upwards, with slopes of 6 6 and 6-6 for the right and left arms, respectively.

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