Question
the graph of a quadratic function is shown on the grid. which function is best represented by the graph?
a f(x) = x^2 + 12
b f(x) = 1/3x^2 + 12
c f(x) = -x^2 - x + 6
d f(x) = -1/3x^2 - x + 6
a f(x) = x^2 + 12
b f(x) = 1/3x^2 + 12
c f(x) = -x^2 - x + 6
d f(x) = -1/3x^2 - x + 6
Answers
GPT-4o mini
To determine which function best represents the graph of a quadratic function, we would typically look for key features such as the direction of the parabola (opens upward or downward), the vertex, and any intercepts.
1. **Opening direction**: If the parabola opens upward, you’ll be looking for a positive coefficient in front of \(x^2\), and if it opens downward, you’ll want a negative coefficient.
2. **Vertex**: The vertex of the parabola is the highest or lowest point. This can give you clues about the function, especially if it's at a specific coordinate you can identify from the graph.
3. **Intercepts**: The \(y\)-intercept can also help to distinguish between functions, particularly if you can observe where the graph crosses the y-axis.
Without the graph provided, I can't give you an exact match, but you can use these steps to analyze the graph.
- If the graph opens upward, the possible functions would be **a** and **b**.
- If it opens downward, the possible functions would be **c** and **d**.
In summary, please look at the opening direction and key points of the graph to match it to one of the given functions.
1. **Opening direction**: If the parabola opens upward, you’ll be looking for a positive coefficient in front of \(x^2\), and if it opens downward, you’ll want a negative coefficient.
2. **Vertex**: The vertex of the parabola is the highest or lowest point. This can give you clues about the function, especially if it's at a specific coordinate you can identify from the graph.
3. **Intercepts**: The \(y\)-intercept can also help to distinguish between functions, particularly if you can observe where the graph crosses the y-axis.
Without the graph provided, I can't give you an exact match, but you can use these steps to analyze the graph.
- If the graph opens upward, the possible functions would be **a** and **b**.
- If it opens downward, the possible functions would be **c** and **d**.
In summary, please look at the opening direction and key points of the graph to match it to one of the given functions.