To find the correct equation of the parabola with the given hint that the leading coefficient is negative, it is essential to analyze the provided options:
- Option 1: \( f(x) = - (x + 2)^2 + 1 \)
- Option 2: \( f(x) = - (x + 2)^2 - 1 \)
- Option 3: \( f(x) = - (x - 2)^2 + 1 \)
- Option 4: \( f(x) = - (x - 2)^2 - 1 \)
Since the leading coefficient is negative, we need to choose an option that contains a negative sign before the squared term. All provided options have this property.
Next, to determine which equation might reflect the characteristics of the parabola:
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Vertex of the parabola: The equation is in vertex form \( f(x) = a(x - h)^2 + k \) where \( (h, k) \) is the vertex.
- For Options 1 and 2, the vertex is at \( (-2, 1) \).
- For Options 3 and 4, the vertex is at \( (2, 1) \).
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Direction of opening: All options open downward because they all have a negative leading coefficient.
The correct answer will depend on the specific properties of the parabola you're considering. If you know the vertex or the value at certain points on the graph, you can eliminate some options.
Without additional context, if we must choose based only on the condition given (having a negative leading coefficient), any of these equations could technically represent the given parabola as long as they match (not given here) with the parabola’s vertex and other characteristics.
Choose the option that best matches the vertex you have information about:
- If \( (-2, 1) \) is the vertex, then choose between Option 1 and Option 2.
- If \( (2, 1) \) is the vertex, then choose between Option 3 and Option 4.
Please provide more details to narrow it down further.
1 answer