Final answer:
The vertex of the parabola represented by the given function f(x) = 3(x-2)² + 4 is (1, 7).
Step-by-step explanation:
The given function is f(x) = 3(x-2)² + 4. To find the vertex of the parabola represented by this function, we can use the formula h = -b/2a and substitute the values of a and b from the standard form ax² + bx + c. In this case, a = 3, b = -6, and c = 4. Plugging these values into the formula, we get h = -(-6)/(2*3) = 6/6 = 1. So, the x-coordinate of the vertex is 1. To find the y-coordinate, we substitute the value of x into the function f(x), giving us f(1) = 3(1-2)² + 4 = 3(-1)² + 4 = 3 + 4 = 7. Therefore, the vertex of the parabola is (1, 7).