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.