Use the table to answer the question. Create an absolute value equation for the graph. (1 point) y=| x+ |

Answer 1

To create an absolute value equation based on a graph, we generally need key information such as the vertex of the graph and any shifts or transformations applied to the basic absolute value function \( y = |x| \).

Since I don't have the specific table or graph you are referencing, I can provide a generic structure for an absolute value equation. Here's how to form such an equation:

1. Identify the vertex (h, k): This is the point where the graph of the absolute value function changes direction. If the vertex is at \((h, k)\), the equation of the absolute value function will be shifted horizontally by \( h \) and vertically by \( k \).

2. Form the equation: The absolute value function can be represented in the form: \[ y = a |x - h| + k \] where \( a \) affects the width and direction (if \( a \) is negative, the graph opens downwards) of the V-shape, \( h \) is the x-coordinate of the vertex, and \( k \) is the y-coordinate of the vertex.

3. Create your specific equation: If you know the values for \( a \), \( h \), and \( k \), you can substitute them into the structure above to get your absolute value equation.

Without the table or any specific graph information, I can’t provide a specific equation. If you can share the relevant values or details from the table, I can help you derive the exact equation!

Answer 2

A V-shaped line passes through 5 plotted points on a coordinate plane. The axes range from negative 10 to 10 in 1-unit increments. The vertex is not plotted.

Answer 3

To create an absolute value equation for a V-shaped graph that passes through five points, we need to establish certain characteristics based on the information provided:

1. Identify the vertex: The vertex of the V-shape is the point where the graph changes direction. Since you mentioned it is not plotted, we or assuming it is somewhere on the coordinate system within the range from -10 to 10.

2. Determine the points: If the five plotted points are known, they will help us find the slope of the lines and the vertex position. Common forms of V-shaped graphs are centered around vertices, which would give them a symmetry.

3. Equation form: The general form for an absolute value function is \[ y = a |x - h| + k \] where \( (h, k) \) is the vertex.

Steps to Formulate the Equation

1. Estimate the Vertex: If you have the five plotted points, look at where they seem to be symmetric around a central point. For instance, if they are concentrated around \( x = 1 \) and \( y = 3 \), then we can assume the vertex might be around (1, 3).

2. Determine the Value of \( a \): The value \( a \) represents the "steepness" of the V. You can calculate it using any two of the five points. The slope of the lines can be found by taking the difference in \( y \) values and the difference in \( x \) values from the vertex to a point.

3. Construct the Equation: Once you have \( h \), \( k \), and \( a \), substitute into the equation: \[ y = a |x - h| + k \]

Example

If we assume the vertex is at (0, 0) and the graph opens upwards, here's how it could look based on your five points:

• Assume your five points are:
  1. (-2, 2)
  2. (2, 2)
  3. (-1, 1)
  4. (1, 1)
  5. (0, 0)

From this, you can see the vertex might be at (0, 0).

If you wanted to determine the slope from one point, for example:

\[ a = \frac{y_1 - k}{x_1 - h} \] If you chose (2, 2): \[ a = \frac{2 - 0}{2 - 0} = 1 \]

Thus, the equation is:

\[ y = |x| \]

Conclusion

To provide you with the exact absolute value equation, you would need to provide the specific coordinates of the five points through which the V-shaped graph passes, as they will guide us to find the vertex and the steepness (the value of \( a \)). If you have those points, please share them for a more precise equation!