Final answer:
The quadratic function with the vertex (2, -3) and the y-intercept (0, 1) is y = (x - 2)^2 - 3.
Step-by-step explanation:
To find the quadratic function given the vertex (2, -3) and the y-intercept (0,1), we can use the vertex form of a quadratic equation which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Since we know the vertex is (2, -3), we can substitute h and k into the equation, giving us y = a(x - 2)^2 - 3.
Next, to determine the value of 'a', we use the fact that the y-intercept is (0,1).
Substituting x = 0 and y = 1 into our equation gives us 1 = a(0 - 2)^2 - 3.
Solving for 'a' gives us a = 1.
Therefore, the quadratic function is y = (x - 2)^2 - 3.