Question
Which equation represents the vertex form of the quadratic function in the graph?
(1 point)
Responses
y=−(x − 1)^2 + 6
y=−(x − 1)^2 + 6
y=−(x − 6)^2 + 1
y=−(x − 6)^2 + 1
y=−(x + 6)^2 −1
y=−(x + 6)^2 −1
y=−(x + 1)^2 −6
(1 point)
Responses
y=−(x − 1)^2 + 6
y=−(x − 1)^2 + 6
y=−(x − 6)^2 + 1
y=−(x − 6)^2 + 1
y=−(x + 6)^2 −1
y=−(x + 6)^2 −1
y=−(x + 1)^2 −6
Answers
Answered by
GPT-4o mini
The vertex form of a quadratic function is given by the equation:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
To determine which equation represents the vertex form of a quadratic function based on the choices provided, we look for the equation that is structured as shown above.
Here are the options you've given and a brief check for each:
1. **y = −(x − 1)^2 + 6**
- This is in the vertex form: vertex at (1, 6).
2. **y = −(x − 6)^2 + 1**
- This is also in the vertex form: vertex at (6, 1).
3. **y = −(x + 6)^2 − 1**
- This is again in the vertex form: vertex at (-6, -1).
4. **y = −(x + 1)^2 − 6**
- This is in the vertex form as well: vertex at (-1, -6).
All of the provided equations are in vertex form, but which one corresponds to the graph you are referencing would depend on the vertex coordinates shown in the graph. You’ll need to look for the vertex from the graph to choose the right equation. If you can provide additional details about the graph (such as the vertex), I can help identify the exact equation that matches.
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
To determine which equation represents the vertex form of a quadratic function based on the choices provided, we look for the equation that is structured as shown above.
Here are the options you've given and a brief check for each:
1. **y = −(x − 1)^2 + 6**
- This is in the vertex form: vertex at (1, 6).
2. **y = −(x − 6)^2 + 1**
- This is also in the vertex form: vertex at (6, 1).
3. **y = −(x + 6)^2 − 1**
- This is again in the vertex form: vertex at (-6, -1).
4. **y = −(x + 1)^2 − 6**
- This is in the vertex form as well: vertex at (-1, -6).
All of the provided equations are in vertex form, but which one corresponds to the graph you are referencing would depend on the vertex coordinates shown in the graph. You’ll need to look for the vertex from the graph to choose the right equation. If you can provide additional details about the graph (such as the vertex), I can help identify the exact equation that matches.