Question

Match the equation with its feature

y = -2 (x + 3)^2 -7
y = 1/2 (x +3) ^2 = 7
y = (x - 3))^2 + 7
y= (x+ 7)^2 -3

Maximum at -7
Axis of symmetry is x = -7
Minimum at -7
Vertex at ( 3, 7)

Answer 1

Let's analyze each equation to match it with its feature:

1. **y = -2 (x + 3)^2 - 7**
- This is a downward-opening parabola (since the coefficient of the squared term is negative).
- Vertex: The vertex form is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, the vertex is at \( (-3, -7) \).
- **Feature: Maximum at -7**

2. **y = 1/2 (x + 3)^2 + 7**
- This is an upward-opening parabola (since the coefficient of the squared term is positive).
- Vertex: Here, the vertex is at \( (-3, 7) \).
- **Feature: Minimum at 7**

3. **y = (x - 3)^2 + 7**
- This is also an upward-opening parabola.
- Vertex: Here, the vertex is at \( (3, 7) \).
- **Feature: Vertex at (3, 7)**

4. **y = (x + 7)^2 - 3**
- This is an upward-opening parabola.
- Vertex: Here, the vertex is at \( (-7, -3) \).
- **Feature: Axis of symmetry is x = -7**

Now let's summarize the matches:

- **y = -2 (x + 3)^2 - 7** → **Maximum at -7**
- **y = 1/2 (x + 3)^2 + 7** → **Minimum at 7**
- **y = (x - 3)^2 + 7** → **Vertex at (3, 7)**
- **y = (x + 7)^2 - 3** → **Axis of symmetry is x = -7**

If necessary, you can adjust based on any additional context you may have!