Question

Match the equation with its feature.(4 points)

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


Axis of Symmertry is x=-7

maximum at -7

vertex at (3,7)

minimum at -7

Answer 1

Let's match each equation with its corresponding feature:

1. **y = −2(x + 3)² − 7**
- This equation opens downward (the coefficient of the squared term is negative).
- **Feature:** maximum at -7

2. **y = 1/2(x + 3)² − 7**
- This equation opens upward (the coefficient of the squared term is positive).
- **Feature:** minimum at -7

3. **y = (x + 7)² − 3**
- This equation opens upward (the coefficient of the squared term is positive). The vertex of this parabola can be found at the point (-7, -3).
- **Feature:** axis of symmetry is x = -7

4. **y = (x − 3)² + 7**
- This equation opens upward (the coefficient of the squared term is positive), and its vertex is at the point (3, 7).
- **Feature:** vertex at (3, 7)

Here’s the final matching:

- **y = −2(x + 3)² − 7** → maximum at -7
- **y = 1/2(x + 3)² − 7** → minimum at -7
- **y = (x + 7)² − 3** → axis of symmetry is x = -7
- **y = (x − 3)² + 7** → vertex at (3, 7)