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Hello!
Recall that the transformations form of a parabola is:
f(x) = ±a(b(x-h)) + k where:
a = vertical stretch/compression
b = horizontal stretch/compression
h = horizontal shift, x-coordinate of vertex
k = vertical shift, y-coordinate of vertex
In this instance, the parent function is f(x) = 3x^2. There is a vertical stretch of 3.
However, there is a point (7, -2) that needs to be included. Substitute these values into the transformation formula:
h = 7
k = -2
f(x) = 3(x - 7)² - 2 is the equation with (7, -2) as the vertex.