Here is the graph of the function $F(x) = 2x^2 - 3x + 1$ based on the table of values. The red points represent the values calculated at specific $x$-coordinates from the table, and the blue curve shows the entire parabola.

Do you have any questions or would you like further details on any part of the solution?

Here are 5 follow-up questions related to this:

1. What is the vertex of the parabola, and how can you calculate it?
2. How do you determine if a parabola opens upwards or downwards?
3. What are the roots of the equation $F(x) = 0$, and how can you find them?
4. Can you rewrite $F(x) = 2x^2 - 3x + 1$ in vertex form?
5. How does the discriminant of a quadratic function help us understand its graph?

Tip: The vertex of a quadratic function $ax^2 + bx + c$ is found using $x = -\frac{b}{2a}$, which can help in graphing and understanding the shape of the parabola.