Question

Match each equation with the correct feature.(4 points)

y=(x+1)2+4
y=(x+4)2−1
y=3(x−4)2−1
y=−12(x−4)2+1

Answer 1

To match each quadratic equation with its correct feature, we can analyze the equations to identify characteristics like the vertex, direction of opening, and the amount of vertical shift.

1. **y = (x + 1)² + 4**
- Vertex: (-1, 4)
- Opens upwards (positive coefficient)
- Feature: Vertex at (-1, 4)

2. **y = (x + 4)² - 1**
- Vertex: (-4, -1)
- Opens upwards (positive coefficient)
- Feature: Vertex at (-4, -1)

3. **y = 3(x - 4)² - 1**
- Vertex: (4, -1)
- Opens upwards (positive coefficient)
- Feature: Vertex at (4, -1) with a vertical stretch (3)

4. **y = -12(x - 4)² + 1**
- Vertex: (4, 1)
- Opens downwards (negative coefficient)
- Feature: Vertex at (4, 1) with a vertical stretch (12) and downwards opening

So the summary is:

1. **y = (x + 1)² + 4** - Vertex at (-1, 4)
2. **y = (x + 4)² - 1** - Vertex at (-4, -1)
3. **y = 3(x - 4)² - 1** - Vertex at (4, -1)
4. **y = -12(x - 4)² + 1** - Vertex at (4, 1) with downward opening

If you need detailed features matched to specific features described in a question (like one feature at a time), please provide those features so I can match them accordingly!