To find the vertex of the quadratic function $y = x^2 - 4x - 10$, we can use the formula for the vertex of a parabola in the form $y = ax^2 + bx + c$:

1. The x-coordinate of the vertex is given by $x = -\frac{b}{2a}$.
2. The y-coordinate can be found by substituting this x-value back into the equation.

Here:

• $a = 1$
• $b = -4$
• $c = -10$

Step 1: Calculate the x-coordinate of the vertex

$x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} = 2$

Step 2: Substitute $x = 2$ into the equation to find the y-coordinate

$y = (2)^2 - 4(2) - 10$ $y = 4 - 8 - 10 = -14$

Conclusion

The vertex is $(2, -14)$, which matches option B.

Would you like further details on this process, or do you have any additional questions?

Here are some related questions you might find useful:

1. How do you determine the vertex of a quadratic function in general?
2. What does the vertex represent in the graph of a parabola?
3. How do you determine if a vertex is a maximum or minimum?
4. What are other ways to find the vertex, like completing the square?
5. How does changing the values of $a$, $b$, or $c$ affect the position of the vertex?

Tip: The vertex form of a quadratic equation, $y = a(x - h)^2 + k$, directly reveals the vertex as $(h, k)$.