Graph y=-2|x|

Problem

y=−2*|x|

Solution

1. Identify the parent function as the absolute value function y=|x| which has a characteristic V-shape with a vertex at (0,0)

2. Apply the vertical stretch by a factor of 2 due to the coefficient 2 which makes the V-shape narrower.

3. Reflect the graph across the x-axis because of the negative sign, changing the orientation from opening upward to opening downward.

4. Determine key points to plot the graph: the vertex is at (0,0) and other points include (1,−2) (−1,−2) (2,−4) and (−2,−4)

5. Draw two rays starting from the vertex (0,0) passing through the calculated points to form a downward-pointing V-shape.

Final Answer

y=−2*|x|

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