Question

Match the equation with its feature.(4 points)
y=(x−3)^2+7

y=−2(x+3)^2−7

y=(x+7)^2−3

y=1/2(x+3)^2−7

Responses

vertex at (3, 7)

axis of symmetry is x = -7

minimum at -7

maximum at -7

Answer 1

Let's match each equation with its corresponding feature:

1. **y = (x − 3)^2 + 7**
- **Feature:** vertex at (3, 7)

2. **y = −2(x + 3)^2 − 7**
- **Feature:** maximum at -7 (because the parabola opens downwards due to the negative coefficient)

3. **y = (x + 7)^2 − 3**
- **Feature:** axis of symmetry is x = -7 (the vertex form shows the axis of symmetry at x = -h, where h is from (x + 7))

4. **y = 1/2(x + 3)^2 − 7**
- **Feature:** minimum at -7 (because the parabola opens upwards due to the positive coefficient)

So the matched responses are:
- y=(x−3)^2+7 → vertex at (3, 7)
- y=−2(x+3)^2−7 → maximum at -7
- y=(x+7)^2−3 → axis of symmetry is x = -7
- y=1/2(x+3)^2−7 → minimum at -7