Use the draggable points to graph y=−2|x−3|+5




To graph the equation \( y = -2|x - 3| + 5 \), you should follow these steps:

1. **Understand the structure of the equation**:
   - \( y = |x - 3| \) represents the basic absolute value function, which is a V-shaped graph with the vertex at \( (3, 0) \).
   - The factor of \( -2 \) reflects and stretches the graph vertically by a factor of 2, making the V open downward and steeper.
   - The \( +5 \) at the end shifts the entire graph up by 5 units.

2. **Determine the vertex**:
   The vertex of the graph is at \( (3, 5) \), because the equation is of the form \( y = -2|x - 3| + 5 \).

3. **Plot key points**:
   - For \( x = 3 \), \( y = 5 \), so plot the point \( (3, 5) \).
   - For \( x = 4 \), calculate \( y = -2|4 - 3| + 5 = -2(1) + 5 = 3 \), so plot \( (4, 3) \).
   - For \( x = 2 \), calculate \( y = -2|2 - 3| + 5 = -2(1) + 5 = 3 \), so plot \( (2, 3) \).
   - As \( x \) moves further away from 3, the absolute value term increases, and the graph continues downward with a slope of \( -2 \) to the left and right of the vertex.

4. **Sketch the V-shape**:
   The graph should form a V with the vertex at \( (3, 5) \), opening downwards and stretching steeper due to the factor of \( -2 \).

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Use the draggable points to graph y=-2|x-3|+5

Learn how to graph the absolute value function y=-2|x-3|+5, including steps for plotting the vertex, applying transformations, and sketching the V-shape. This problem is suitable for students in Grades 8-10, covering essential concepts in graphing and function transformations.

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