To find the vertex form of a parabola based on a graph, we typically look for the vertex \((h, k)\) of the parabola, which is represented in the form \(y = a(x - h)^2 + k\). The coefficient \(a\) indicates the direction (upward or downward) and the width of the parabola.
Without viewing the actual graph, I can help you determine which of the given equations is correct based on the vertex and the direction of the opening:
- Identify the vertex: Look for the highest or lowest point of the parabola, which is the vertex.
- Determine the value of \(a\): If the parabola opens downward, \(a\) will be negative. If it opens upward, \(a\) will be positive.
As for these equations:
- \(y = -2(x - 1)^2 + 3\) opens downward, vertex at \((1, 3)\).
- \(y = -2(x + 1)^2 - 3\) opens downward, vertex at \((-1, -3)\).
- \(y = 3(x + 1)^2 - 3\) opens upward, vertex at \((-1, -3)\).
- \(y = 3(x - 1)^2 + 3\) opens upward, vertex at \((1, 3)\).
If you were able to see the graph, match the features of the parabola (particularly the vertex and the direction it opens) to determine the correct option.
If the vertex is at \((1, 3)\) and opens downward, the correct equation would be: \(y = -2(x - 1)^2 + 3\).
Please confirm the graph features for accurate selection!
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