To determine the x-coordinate of the vertex of the quadratic function $f(x) = ax^2 + bx + c$, where $a \neq 0$, we use the formula for the vertex of a parabola given by the quadratic function. The x-coordinate of the vertex is given by:

$x = -\frac{b}{2a}$

So, the complete sentence would be:

The x-coordinate of the vertex of $f(x) = ax^2 + bx + c$, $a \neq 0$, is $-\frac{b}{2a}$.

Would you like more details or have any questions?

Here are 5 numbered questions for you to ask:

1. What is the formula for finding the y-coordinate of the vertex of a quadratic function?
2. How do you determine if a quadratic function opens upwards or downwards?
3. Can you explain how to complete the square for a quadratic equation?
4. What are the steps to derive the quadratic formula?
5. How can you find the roots of a quadratic equation using factoring?

Tip: Always check the sign of the coefficient $a$ in a quadratic function to determine the direction in which the parabola opens. If $a > 0$, it opens upwards; if $a < 0$, it opens downwards.