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The graph provided is a V-shaped graph, which resembles the basic function \( y = |x| \). This is a well-known absolute value function that typically has its vertex at the origin (0, 0). However, in this graph, the vertex of the function has been translated downwards to the point (0, -4).

To find the equation of the translated function:

1. Start with the basic absolute value function: \( y = |x| \).
2. The translation downward by 4 units means we subtract 4 from the basic function.

So, the equation that defines the function is:

\[
y = |x| - 4
\]

Would you like any further details or have any questions? Here are some related questions:

1. What happens to the graph of \( y = |x| \) if you translate it to the right by 3 units?
2. How would the graph change if the translation was 4 units upward instead of downward?
3. What is the effect of translating the graph of \( y = |x| \) to the left by 2 units?
4. How would you write the equation if the vertex was at (-3, 4)?
5. Can you explain how to determine the vertex of the graph just by looking at the equation \( y = |x| + c \)?

**Tip:** When translating graphs, remember that translations vertically (up or down) affect the constant term outside the function, while horizontal translations (left or right) affect the input variable \( x \) inside the function.

The graph is a translation of one of the basic functions: y = x^2, y = x^3, y = √x, y = |x|. Find the equation that defines the function.

Explore how to translate the basic absolute value function y = |x|. This example demonstrates a translation of 4 units downward, resulting in the equation y = |x| - 4. Suitable for students in Grades 8-10.

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