To write the equation of the quadratic function in vertex form \( y = a(x - h)^2 + k \), we need to identify the vertex \((h, k)\) and the value of \(a\).
From your description:
- The vertex is at the highest point of the parabola, which occurs at the point \((2, -2)\) based on your description that it "curves up from -2, stops at 2 then curves back down."
- The value of \(a\) can be determined by another point on the parabola. If we assume the parabola passes through another point, we can calculate \(a\) using that point. However, we do not have another specific point provided apart from the vertex; thus, we usually either need a point below the vertex or a curvature height at a certain x-value to determine \(a\).
If we assume a value for \(a\) just for completion (let’s check \(a = -1/2\) as per your preference):
The vertex form of the quadratic would look like this when substituting:
- \((h, k) = (2, -2)\)
- Set \(a = -1/2\):
Thus, the equation in vertex form:
\[ y = -\frac{1}{2}(x - 2)^2 - 2 \]
So in your requested format:
\[ y = -\frac{1}{2}(x - 2)^2 - 2 \]
Hence, \(h = 2\) and \(k = -2\).
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