To write the vertex form of a parabola that opens upward, we use the formula:
\[ y = a(x-h)^2 + k \]
where \((h, k)\) is the vertex of the parabola, and \(a\) is a coefficient that determines how "wide" or "narrow" the parabola is and whether it opens upwards or downwards.
Given that the parabola curves upward and has a vertex at the point (2, -14), we can substitute \(h = 2\) and \(k = -14\) into the vertex form. This gives us:
\[ y = a(x - 2)^2 - 14 \]
Next, to determine the value of \(a\), we would need another point on the parabola. However, since only the vertex point has been provided in your case, we cannot find the exact value of \(a\) without additional information.
So, the vertex form of the equation based on the information provided is:
\[ y = a(x - 2)^2 - 14 \]
Where \(a\) is a positive number (since the parabola opens upward). If you have another point that lies on the graph, you can substitute it into the equation to solve for \(a\).
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