The vertex of the parabola defined by $f(x) = ax^2 + bx + c$ is the point:

$\left( \frac{-b}{2a}, \ f\left( \frac{-b}{2a} \right) \right)$

So, the coordinates of the vertex are $\left( \frac{-b}{2a}, \frac{4ac - b^2}{4a} \right)$.

Would you like further explanation on how this formula is derived?

Here are 5 related questions to explore:

1. How do you find the vertex from the standard form $f(x) = a(x - h)^2 + k$?
2. What does the value of $a$ tell you about the direction of the parabola?
3. How can you determine the axis of symmetry for the parabola?
4. How do you convert from standard form $f(x) = ax^2 + bx + c$ to vertex form $f(x) = a(x - h)^2 + k$?
5. What is the significance of the discriminant $b^2 - 4ac$ in determining the nature of the parabola's roots?

Tip: The x-coordinate of the vertex is always located on the parabola's axis of symmetry!