To write the equation of a quadratic function in vertex form, we need to identify the vertex of the parabola from the graph. The vertex form of a quadratic function is:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex and \(a\) represents the vertical stretch or compression of the parabola.
From your description, it seems like the parabola opens downwards (since the value of \(a\) is negative, \(a = -1/2\)).
To complete the equation, we need to find the vertex \((h, k)\) of the parabola. The values should be extracted directly from the graph, but since I can't see the image, I will provide a general template based on what you should look for:
- Identify the x-coordinate of the vertex (\(h\)).
- Identify the y-coordinate of the vertex (\(k\)).
Once you have those values:
- Substitute \(h\) and \(k\) into the equation:
\[ y = -\frac{1}{2}(x - h)^2 + k \]
For example, if from the graph you determine the vertex is at the point (3, 2), the equation would be:
\[ y = -\frac{1}{2}(x - 3)^2 + 2 \]
Please find the vertex's exact coordinates from the graph and replace \(h\) and \(k\) in the equation above to get your specific quadratic function in vertex form.
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