Here's the graph of the function $f(x) = 3x^2 - 4x + 1$.

Do you want details on how the function was plotted or have any questions?

Here are some related questions to consider:

1. What are the vertex and axis of symmetry for this quadratic function?
2. How do we determine the direction of the parabola’s opening?
3. Can we calculate the x-intercepts (roots) of this function?
4. How would changing the coefficient of $x^2$ affect the shape of the graph?
5. What is the minimum or maximum value of this function, and where does it occur?

Tip: For quadratic functions, the coefficient of $x^2$ dictates the parabola's width and direction.