https://file.aiquickdraw.com/mathbot/file/1724812778742mnss5x24.jpg

The image you provided contains a table and a question. However, the text is somewhat distorted. I'll do my best to interpret it.

The question appears to ask for a graph of certain data points related to a function \( f(x) = x^2 - 2x \) over the interval \( x = -2 \) to \( x = 2 \). The table seems to include values of \( x \) and corresponding values of \( y = f(x) \).

Here are the points that you likely need to graph based on the function:

- \( x = -2 \), \( y = f(-2) = (-2)^2 - 2(-2) = 4 + 4 = 8 \)
- \( x = -1 \), \( y = f(-1) = (-1)^2 - 2(-1) = 1 + 2 = 3 \)
- \( x = 0 \), \( y = f(0) = 0^2 - 2(0) = 0 \)
- \( x = 1 \), \( y = f(1) = 1^2 - 2(1) = 1 - 2 = -1 \)
- \( x = 2 \), \( y = f(2) = 2^2 - 2(2) = 4 - 4 = 0 \)

So, the points you need to plot are:

\[
(-2, 8), (-1, 3), (0, 0), (1, -1), (2, 0)
\]

Would you like any further details or explanations on how to graph these points? 

Here are some follow-up questions you might consider:
1. What is the general shape of the graph for a quadratic function like \( f(x) = x^2 - 2x \)?
2. How do you find the vertex of the parabola from the equation?
3. What is the axis of symmetry for the graph of \( f(x) = x^2 - 2x \)?
4. How can you determine the direction of the parabola (upward or downward)?
5. What are the implications of the interval \( x = -2 \) to \( x = 2 \) for graphing?

**Tip:** When graphing a quadratic function, always identify the vertex and axis of symmetry first to better understand the graph's overall shape.

Learn how to graph the quadratic function f(x) = x^2 - 2x over the interval x = -2 to x = 2. This problem involves identifying key points (x, f(x)) and understanding the shape of the parabola. Suitable for high school students.

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