Find a quadratic function $\mathrm{f}$ whose graph matches the one below.
Vertex = (-2,3) and passes through point (0,-1)

Step 1 ：The general form of a quadratic function is \(f(x) = a(x-h)^2 + k\), where (h,k) is the vertex of the parabola.

Step 2 ：We know the vertex is (-2,3), so we can substitute h = -2 and k = 3 into the equation.

Step 3 ：We also know that the function passes through the point (0,-1), so we can substitute x = 0 and f(x) = -1 into the equation to solve for a.

Step 4 ：Substituting these values into the equation gives us \(f = a*(x + 2)^2 + 3\)

Step 5 ：Setting this equal to -1 gives us the equation \(eq = 4*a + 3 = -1\)

Step 6 ：Solving this equation gives us a value of a = -1

Step 7 ：Substituting a = -1 back into the original equation gives us the final quadratic function

Step 8 ：\(\boxed{f(x) = -1(x+2)^2 + 3}\)