Question

Match each equation with its feature in the options.
Equations:
y = 1/2 (x + 3)^2 - 7
y = -2 (x + 3)^2 - 7
y = (x - 3)^2 + 7
y = (x + 7)^2 - 3
Options:
Axis of Symmetry is: x = -7
Maximum at: -7
Vertex at: (3, 7)
Minimum at: -7

Answer 1

Let's analyze each equation to match them with their corresponding features:

1. **Equation: y = 1/2 (x + 3)^2 - 7**
- This is a quadratic equation in vertex form. The vertex can be identified as:
- Vertex: (-3, -7)
- Since the coefficient of the quadratic term (1/2) is positive, it means this parabola opens upwards, so it has a minimum point.
- **Feature: Minimum at: -7**

2. **Equation: y = -2 (x + 3)^2 - 7**
- This is also in vertex form. The vertex is:
- Vertex: (-3, -7)
- The coefficient (-2) is negative, meaning this parabola opens downwards, which results in a maximum point.
- **Feature: Maximum at: -7**

3. **Equation: y = (x - 3)^2 + 7**
- This is a quadratic equation where:
- Vertex: (3, 7)
- Since the coefficient (1) is positive, it means this parabola opens upwards, indicating that it has a minimum point.
- **Feature: Vertex at: (3, 7)**

4. **Equation: y = (x + 7)^2 - 3**
- This is a quadratic equation:
- Vertex: (-7, -3)
- The coefficient (1) is positive, indicating that this parabola opens upwards, so it has a minimum point.
- **Feature: Axis of Symmetry is: x = -7**

Now let's match all the equations to the features:
1. \( y = 1/2 (x + 3)^2 - 7 \) - **Minimum at: -7**
2. \( y = -2 (x + 3)^2 - 7 \) - **Maximum at: -7**
3. \( y = (x - 3)^2 + 7 \) - **Vertex at: (3, 7)**
4. \( y = (x + 7)^2 - 3 \) - **Axis of Symmetry is: x = -7**