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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.

Learn how to determine the x-coordinate of the vertex of a quadratic function f(x) = ax^2 + bx + c using the vertex formula x = -b/(2a). This problem involves key concepts in quadratic functions and is suitable for high school students.

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