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To find the vertex of the quadratic function \( f(x) = 2x^2 - 4x - 6 \), we can use the vertex formula for a parabola given by \( f(x) = ax^2 + bx + c \). The x-coordinate of the vertex is calculated using:

\[
x = -\frac{b}{2a}
\]

For the given function \( f(x) = 2x^2 - 4x - 6 \):
- \( a = 2 \)
- \( b = -4 \)

Let's find the x-coordinate:

\[
x = -\frac{-4}{2 \cdot 2} = \frac{4}{4} = 1
\]

Now, substitute \( x = 1 \) back into the function to find the y-coordinate:

\[
f(1) = 2(1)^2 - 4(1) - 6 = 2 - 4 - 6 = -8
\]

So, the vertex of the function is at \((1, -8)\).

The correct answer is:
- \((1, -8)\)

Would you like more details or have any questions? Here are some related questions:

1. How do you derive the vertex formula \( x = -\frac{b}{2a} \)?
2. What is the significance of the vertex in the graph of a parabola?
3. How can you determine whether a parabola opens upward or downward?
4. What role does the coefficient \( a \) play in the shape of a quadratic function?
5. How do you convert a quadratic function into vertex form?

**Tip:** The vertex form of a quadratic function, \( f(x) = a(x - h)^2 + k \), makes it easier to identify the vertex, where \((h, k)\) is the vertex.

Which is the vertex of the quadratic function f(x) = 2x^2 - 4x - 6?

This page explains how to find the vertex of the quadratic function f(x) = 2x^2 - 4x - 6 using the vertex formula and standard form of a quadratic equation. Suitable for students in Grades 9-12.

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