The given function is:

$f(x) = 2x^2 + 4x + 6$

This is a quadratic function. Would you like to analyze its properties, such as finding its vertex, roots, or derivative?

Here are five follow-up questions that could be helpful:

1. Would you like to solve for the roots of the quadratic equation $f(x) = 0$?
2. Are you interested in finding the vertex of this parabola?
3. Would you like to calculate the derivative of this function?
4. Would you like to determine the axis of symmetry of the quadratic function?
5. Should we graph the function to visualize its shape?

Tip: The discriminant of a quadratic equation, $b^2 - 4ac$, helps determine the nature of the roots.