The function you provided is a quadratic function in vertex form:
\[ f(x) = -3(x - 5)^2 + 7. \]
This function opens downwards (since the coefficient of the squared term is negative), which means it has a maximum point rather than a minimum point.
The vertex of the function occurs at \((h, k)\), where \(h\) and \(k\) are the values in the vertex form \(f(x) = a(x - h)^2 + k\). In this case:
- \(h = 5\)
- \(k = 7\)
Thus, the coordinates of the maximum point (the vertex of the parabola) are \((5, 7)\).
If you were looking for the minimum point of a square root function related to this quadratic function, please specify the square root function so that I can provide accurate coordinates for that. Otherwise, for the given quadratic function \(f(x) = -3(x - 5)^2 + 7\), the coordinates of the maximum point are \((5, 7)\).
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