https://file.aiquickdraw.com/mathbot/file/1725493339109ha2r8q4x.jpg

The equation in the image is \( x^2 - y = 0 \), which can be rewritten as:

\[
y = x^2
\]

This is the equation of a parabola that opens upwards, with the vertex at the origin \((0, 0)\). The graph shows that the parabola passes through points like \((1, 1)\) and \((-1, 1)\).

### Key points:
1. **Vertex**: The vertex is at the origin, \((0, 0)\).
2. **Symmetry**: The parabola is symmetric about the y-axis, as \( x^2 \) is an even function.
3. **Direction**: The parabola opens upwards because of the positive coefficient of \( x^2 \).
4. **Shape**: The points \((1, 1)\), \((-1, 1)\), and other symmetrical points follow the pattern of a standard parabola.

Would you like a more detailed explanation, or do you have specific questions about this parabola?

Here are 5 related questions to consider:
1. What is the effect of changing the coefficient of \( x^2 \) on the graph of the parabola?
2. How would the graph change if the equation was \( x^2 - y = 1 \)?
3. What would the graph look like if the equation was \( -x^2 = y \)?
4. How can we find the focus and directrix of the parabola \( y = x^2 \)?
5. How do we find the axis of symmetry for any given parabola?

**Tip**: Parabolas with equations in the form \( y = ax^2 \) get wider as \( |a| \) decreases and narrower as \( |a| \) increases.

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

Learn how to graph the parabola for the equation x^2 - y = 0 with this detailed step-by-step explanation. Understand the key concepts of algebra, graphing parabolas, and quadratic equations, suitable for students in Grades 8-10.

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