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The vertex of a quadratic function in the form h = at^2 + bt + c is given by (-b/2a, f(-b/2a)), where f(x) represents the function. In this case, the quadratic function is h = 6t^2 - 24t + 30.
To find the vertex, we can first determine the values of a, b, and c. In this case, a = 6, b = -24, and c = 30.
Using the formula for the x-coordinate of the vertex, we have:
x = -b/2a
x = -(-24) / (2*6)
x = 24 / 12
x = 2
To find the y-coordinate of the vertex, we substitute the value of x into the function:
h = 6(2)^2 - 24(2) + 30
h = 6(4) - 48 + 30
h = 24 - 48 + 30
h = 54 - 48
h = 6
Therefore, the vertex is (2, 6).
The correct answer is: (2, 6)