https://file.aiquickdraw.com/mathbot/file/1725493313921sn92qz1f.jpg

The equation provided in the image is \( x^2 - y = 0 \), which can be rewritten as \( y = x^2 \). This represents a parabola that opens upwards with its vertex at the origin, \( (0, 0) \).

Looking at the graph:
- The vertex is at the point \( (0, 0) \), as expected.
- The parabola is symmetric about the y-axis because the equation \( y = x^2 \) is even. This means for every positive \( x \), there is a corresponding negative \( x \) with the same \( y \)-value.
- As \( x \) increases in magnitude (positive or negative), \( y \) grows quadratically.

Do you want more details about the graphing process or any further clarifications?

Here are 5 questions that can expand this topic:
1. What are the key features of the graph of \( y = x^2 \)?
2. How would the graph change if the equation were \( y = -x^2 \)?
3. Can you describe the domain and range of the function \( y = x^2 \)?
4. How would you find the focus and directrix of the parabola \( y = x^2 \)?
5. How does the graph of \( y = x^2 \) compare to \( y = x^3 \)?

**Tip:** The graph of \( y = x^2 \) is a standard parabola. It's useful to remember that all parabolas of the form \( y = ax^2 \) open upwards if \( a > 0 \) and downwards if \( a < 0 \).

Graph the equation of the parabola, x^2 - y = 0.

Explore how to graph the parabola given by x^2 - y = 0, which represents a standard upward-opening parabola. Learn key features like the vertex, symmetry, and growth rate. Suitable for students in Grades 7-9.

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