Final answer:
To find the equation of the quadratic function, consider the shape, line of symmetry, and the y-intercept. Use the given information to determine the equation.
Step-by-step explanation:
To find the equation of the quadratic function, we need to consider each requirement separately. First, we know that the function has the same shape as y=3x², so the leading coefficient is 3. Second, we know that it has the same line of symmetry as y=(x-2)²+3, so the vertex is at x=2. Finally, we know that it cuts the y-axis at a given point. Let's assume that point is (0, k). Plugging in these values into the equation y=a(x-h)²+k, we get y=3(x-2)²+k. Since the function cuts the y-axis at (0, k), we know that k is the y-intercept. So, the equation of the quadratic function is y=3(x-2)²+k, where k is the y-intercept at (0, k).