Select ALL of the equations that have a vertex at (3, 2). Oy = x- 6r + 11 Oy = (x+ 2) (r-3) %3D Oy= (z- 3)+ Oy = r +6r + 9

Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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**Quadratic Equations and Vertices**

**Question:**

Select ALL of the equations that have a vertex at (3, 2).

1. \( y = x^2 - 6x + 11 \)
2. \( y = (x + 2)(x - 3) \)
3. \( y = (x - 3)^2 + 2 \)
4. \( y = x^2 + 6x + 9 \)

**Explanation:**
In this question, you are asked to identify which of the given quadratic equations have a vertex at the point (3, 2). To solve this, consider the different forms of quadratic equations and how to determine their vertices.

**Graph Interpretation:**
- There are no graphs or diagrams provided with this question. 

**Note:** To find the vertex of a quadratic function in standard form \( ax^2 + bx + c \), you can use the vertex formula \( x = -\frac{b}{2a} \) to find the x-coordinate, and then substitute it back into the equation to find the y-coordinate. Quadratic functions in the vertex form \( y = a(x - h)^2 + k \) directly give the vertex as \( (h, k) \).
Transcribed Image Text:**Quadratic Equations and Vertices** **Question:** Select ALL of the equations that have a vertex at (3, 2). 1. \( y = x^2 - 6x + 11 \) 2. \( y = (x + 2)(x - 3) \) 3. \( y = (x - 3)^2 + 2 \) 4. \( y = x^2 + 6x + 9 \) **Explanation:** In this question, you are asked to identify which of the given quadratic equations have a vertex at the point (3, 2). To solve this, consider the different forms of quadratic equations and how to determine their vertices. **Graph Interpretation:** - There are no graphs or diagrams provided with this question. **Note:** To find the vertex of a quadratic function in standard form \( ax^2 + bx + c \), you can use the vertex formula \( x = -\frac{b}{2a} \) to find the x-coordinate, and then substitute it back into the equation to find the y-coordinate. Quadratic functions in the vertex form \( y = a(x - h)^2 + k \) directly give the vertex as \( (h, k) \).
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