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 $(3, 2)$.

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!