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To solve the equation \(x^2 = |x - 2|\) graphically, we need to understand that this equation involves both a quadratic function and an absolute value function. Here's how we can approach it:

1. **Graph \(y = x^2\)**: This is a standard parabola that opens upwards with its vertex at the origin \((0, 0)\).

2. **Graph \(y = |x - 2|\)**: This is a V-shaped graph with a vertex at \(x = 2\). It shifts the absolute value function two units to the right.

To solve \(x^2 = |x - 2|\), we're looking for the points where these two graphs intersect. These intersection points represent the solutions to the equation.

By inspecting the choices and solving:

- Graphically, one of the solutions will be \(x = 2\), as both functions equal zero at this point.
- We also need to check where else the graphs intersect. It turns out that the graphs also intersect at \(x = 0\).

So, the solutions are \(x = 2\) and \(x = 0\), which corresponds to option **F**.

Would you like a detailed breakdown of the graph or any other clarifications?

Here are 5 questions for further exploration:
1. How do you graph absolute value functions in general?
2. What happens when you shift a parabola horizontally or vertically?
3. Can we solve this equation algebraically rather than graphically?
4. What is the role of the vertex in understanding the behavior of quadratic and absolute value functions?
5. How do we know when an equation will have two solutions, one solution, or none?

**Tip**: When solving equations with absolute values, consider breaking them into cases where the inside of the absolute value is both positive and negative.

This guide explains how to solve the equation x^2 = |x - 2| by graphing. Learn how the quadratic and absolute value functions intersect, providing the solutions x = 0 and x = 2. Perfect for students in Grades 8-10 studying algebra.

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