Graph the equation by translating y = |x|.
y = |x + 7|
To graph the equation y = |x + 7|, we can follow these steps:
1. Identify the vertex: In the general form of the equation for an absolute value function, y = |x + h| + k, the vertex is located at the point (-h, k). In this case, h = -7. So, the vertex is at (-(-7), 0), which simplifies to (7, 0).
2. Plot the vertex: On your graph, mark the point (7, 0).
3. Determine other key points: Since we are dealing with the absolute value function, we need to consider both positive and negative values of x to cover all possibilities. Let's choose a few values of x and substitute them into the equation to find the corresponding y-values:
- For x = -7, y = |(-7) + 7| = |0| = 0
- For x = 0, y = |0 + 7| = |7| = 7
- For x = 3, y = |3 + 7| = |10| = 10
4. Plot the additional points: On the graph, plot the points (-7, 0), (0, 7), and (3, 10).
5. Connect the points: Use a straight line to connect the points on the graph. Since we are dealing with the absolute value function, the graph will consist of two straight lines connected at the vertex. One line will be to the right (increasing side) of the vertex, and the other line will be to the left (decreasing side) of the vertex.
Your final graph will look like a "V" shape with the vertex at (7, 0) and the lines extending upwards and downwards from the vertex, passing through the points (-7, 0), (0, 7), and (3, 10).