Question

Match each equation.
With the correct feature
y = - 1/2 (x -4)^2 + 1
y = (x + 4)^2 -1
y =3(x - 4)^2 -1
y = (x + 1)^2 +4

Vertex at (4,-1)
Axis of symmetry at x = -4
Maximum at 1
Minimum at 4

Answer 1

Let's match each equation with the correct feature based on the vertex, axis of symmetry, maximum, and minimum characteristics of the parabolas.

1. **y = \(-1/2 (x - 4)^2 + 1\)**
- Vertex: (4, 1)
- Feature: **Maximum at 1**

2. **y = \((x + 4)^2 - 1\)**
- Vertex: (-4, -1)
- Feature: **Axis of symmetry at x = -4**

3. **y = \(3(x - 4)^2 - 1\)**
- Vertex: (4, -1)
- Feature: **Vertex at (4, -1)**

4. **y = \((x + 1)^2 + 4\)**
- Vertex: (-1, 4)
- Feature: **Minimum at 4**

Here's the final match:

- **y = -1/2 (x - 4)^2 + 1** → **Maximum at 1**
- **y = (x + 4)^2 - 1** → **Axis of symmetry at x = -4**
- **y = 3(x - 4)^2 - 1** → **Vertex at (4, -1)**
- **y = (x + 1)^2 + 4** → **Minimum at 4**