To determine the correct vertex form of the parabolic equation based on the given information, we need to identify the vertex of the parabola and the direction in which it opens.
The vertex form of a parabola is given by the equation:
\[ y = a(x-h)^2 + k \]
where \((h, k)\) is the vertex of the parabola and \(a\) determines the direction and width of the parabola.
- The parabola opens upwards, indicating that \(a\) should be positive.
- The point of intersection with the y-axis and the vertex can be inspected to find the coordinates of the vertex.
Given the options:
- y=2(x+4)²+8: Vertex is at \((-4, 8)\) and opens upwards.
- y=2(x−4)²−8: Vertex is at \((4, -8)\) and opens upwards.
- y=2(x−4)²+8: Vertex is at \((4, 8)\) and opens upwards.
- y=−2(x−4)²+8: Vertex is at \((4, 8)\) but opens downwards.
From analyzing the given options, if the parabola opens upwards, the correct vertex form would be one of the first three options.
Assuming you are able to see the graph and can confirm the vertex location, choose the equation that corresponds to that location accordingly.
If the vertex were located at \((-4, 8)\) or \((4, 8)\), then you would select one of the first two options. Based on typical scenarios, if the vertex appears at either of those two points in the upward-opening context, you would select from options 1 or 3.
Without seeing the image but working from standard form conventions, the most likely candidate is:
- If \((-4, 8)\): y=2(x+4)²+8
- If \((4, 8)\): y=2(x−4)²+8
Be sure to evaluate the graph to confirm the vertex coordinates.
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