To write the vertex form of a parabola, we use 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.
From your description, the parabola opens downward and the y-coordinate indicates that \(a\) is negative.
To fill in the vertex form equation, you need to identify the vertex coordinates \((h, k)\) from the graphical representation of the parabola. Since I cannot see the image, I'll guide you through how to do it:
- Find the vertex of the parabola from the graph. This will be the point where the parabola reaches its maximum (since it opens downward).
- Identify the value of \(k\), which is the y-coordinate of the vertex.
- Identify the value of \(h\), which is the x-coordinate of the vertex.
- Determine the value of \(a\) by finding the width of the parabola. If you have two points on the parabola, you can calculate \(a\) using the standard form of the parabola.
Once you have those values, substitute \(h\), \(k\), and \(a\) into the equation:
\[ y = a(x - h)^2 + k \]
If you provide me with the coordinates of the vertex and the value for \(a\), I can help you complete the vertex form equation!
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