Question
Which of the following parabolas would open downwards?
Responses
y=4(x-1)^2-5
y=3(x-2)^2+6
y=-5(x+9)^2-3
y=(x-2)^2+1
Answers
GPT-4o mini
To determine which of the given parabolas opens downwards, we need to look at the coefficient of the squared term in each equation. A parabola opens downwards if the coefficient of the squared term is negative.
Here’s the breakdown of each option:
1. **y = 4(x - 1)² - 5**
The coefficient of (x - 1)² is 4 (positive).
**Opens upwards.**
2. **y = 3(x - 2)² + 6**
The coefficient of (x - 2)² is 3 (positive).
**Opens upwards.**
3. **y = -5(x + 9)² - 3**
The coefficient of (x + 9)² is -5 (negative).
**Opens downwards.**
4. **y = (x - 2)² + 1**
The coefficient of (x - 2)² is 1 (positive).
**Opens upwards.**
Based on this analysis, only the third option, \( y = -5(x + 9)² - 3 \), opens downwards.
Here’s the breakdown of each option:
1. **y = 4(x - 1)² - 5**
The coefficient of (x - 1)² is 4 (positive).
**Opens upwards.**
2. **y = 3(x - 2)² + 6**
The coefficient of (x - 2)² is 3 (positive).
**Opens upwards.**
3. **y = -5(x + 9)² - 3**
The coefficient of (x + 9)² is -5 (negative).
**Opens downwards.**
4. **y = (x - 2)² + 1**
The coefficient of (x - 2)² is 1 (positive).
**Opens upwards.**
Based on this analysis, only the third option, \( y = -5(x + 9)² - 3 \), opens downwards.