Here is the graph of the function $f(x) = 2 + 3x^2$. The parabola opens upwards, with its vertex at $(0, 2)$ and increasing steeply due to the coefficient of $x^2$ being 3.

Would you like more details or have any specific questions?

Here are some related questions to explore further:

1. How does the value of the coefficient 3 affect the steepness of the parabola?
2. What would happen to the graph if we change the constant term (2) to a different value?
3. How would the graph change if we introduced a linear term like $bx$ in the equation?
4. Can you determine the axis of symmetry for this graph?
5. How do you find the roots of this quadratic function?

Tip: The vertex form of a quadratic function provides an easy way to identify the vertex, making graphing simpler.