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Let's break down the questions you shared from the image:

### Question 2:
The formula \( x = -\frac{b}{2a} \) is used to find:
- This formula is used to find the **x-value of the vertex** of a quadratic function written in the form \( y = ax^2 + bx + c \).

The correct answer for Question 2 is:
- **The x-value of the vertex.**

### Question 3:
To find the vertex of the quadratic function \( y = x^2 - 6x + 11 \):

1. The x-value of the vertex is found using the formula:
   \[
   x = -\frac{b}{2a}
   \]
   For the equation \( y = x^2 - 6x + 11 \), \( a = 1 \) and \( b = -6 \). Substituting these into the formula:
   \[
   x = -\frac{-6}{2(1)} = \frac{6}{2} = 3
   \]

2. To find the y-value, substitute \( x = 3 \) back into the original equation:
   \[
   y = (3)^2 - 6(3) + 11 = 9 - 18 + 11 = 2
   \]

Thus, the vertex is \( (3, 2) \).

The correct answer for Question 3 is:
- The vertex is \( (3, 2) \).

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Would you like more details on any of these solutions? Here are some related questions to explore:

1. What is the significance of the vertex in a quadratic graph?
2. How do you find the axis of symmetry from the vertex form of a quadratic function?
3. Can the vertex formula be used for equations that are not quadratic?
4. How does the value of 'a' in \( y = ax^2 + bx + c \) affect the shape of the parabola?
5. What are other methods to find the vertex of a quadratic function?

### Tip:
The quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) can be used to find the roots (zeros) of a quadratic function, not the vertex!

Question 2: The formula x = -b/2a is used to find _________. Options: the x-value of the vertex, the roots, the y-intercept, the axis of symmetry. 
Question 3: What is the vertex of the quadratic function y = x^2 - 6x + 11?

Learn how to determine the vertex of quadratic functions using the formula x = -b/2a. This guide provides a step-by-step solution for identifying the x-value of the vertex and finding the vertex of the function y = x^2 - 6x + 11. Suitable for Grades 9-10 students.

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