The given function is \( F(x) = x^2 \). This is a quadratic function, and its graph is a parabola.

### Key features of this function:
1. **Domain**: The function is defined for all real numbers, so the domain is \( (-\infty, \infty) \).
2. **Range**: Since \( x^2 \) is always non-negative, the range is \( [0, \infty) \).
3. **Vertex**: The vertex of the parabola is at \( (0, 0) \), which is the lowest point on the graph.
4. **Axis of symmetry**: The axis of symmetry is the vertical line \( x = 0 \).
5. **Intercepts**: 
   - The **x-intercept** is at \( (0, 0) \).
   - The **y-intercept** is also at \( (0, 0) \).

### Behavior:
- As \( x \to \infty \), \( F(x) \to \infty \).
- As \( x \to -\infty \), \( F(x) \to \infty \).

Would you like a detailed explanation of any specific part?

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**Related questions:**
1. How would the function change if the equation was \( F(x) = -x^2 \)?
2. What is the derivative of \( F(x) = x^2 \)?
3. How would you find the area under the curve of \( F(x) = x^2 \) from \( x = 0 \) to \( x = 1 \)?
4. What is the significance of the vertex in the graph of \( F(x) = x^2 \)?
5. How does the graph of \( F(x) = x^2 \) compare to \( F(x) = x^2 + 3 \)?

**Tip**: The derivative of any quadratic function \( ax^2 + bx + c \) gives its slope at any point, which can help understand how the graph changes.

Explore the quadratic function F(x) = x^2. This tutorial covers key features like the domain, range, vertex, and axis of symmetry. Perfect for students in Grades 9-10 looking to understand graphing and properties of parabolas.

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