Simmons Paul
01/19/2024 · Middle School

\( 1 \leftarrow \) Write an absolute value equation for the graph shown to the right.

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To write an absolute value equation for a graph, we need to identify key features of the graph, such as the vertex (the highest or lowest point), the direction it opens (upward or downward), and any transformations (shifts, stretches, or reflections). Assuming the graph is a standard V-shape (which is typical for absolute value functions), the general form of an absolute value equation is: \[ y = a |x - h| + k \] where: - \( (h, k) \) is the vertex of the graph, - \( a \) determines the direction and steepness of the graph (if \( a > 0 \), it opens upwards; if \( a < 0 \), it opens downwards). To write the specific equation, you would need to provide the coordinates of the vertex and any other points on the graph to determine the value of \( a \). For example, if the vertex of the graph is at the point \( (2, 3) \) and the graph opens upwards, the equation would start as: \[ y = a |x - 2| + 3 \] If you know another point on the graph, you can substitute the coordinates of that point into the equation to solve for \( a \). Please provide more details about the graph, such as the vertex and any other points, so I can help you write the exact equation.

Quick Answer

The general form of an absolute value equation is \( y = a |x - h| + k \), where \( (h, k) \) is the vertex. To find the specific equation, you need the vertex and another point on the graph.
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