A quadratic equation with vertex (-2, 5) is : y = a(x + 2)^2 + 5

As it passes through (0, 9), 9 = a(0 + 2)^2 + 5

=> 9 = 4a + 5

=> a = 1

The equation of the quadratic function is y = (x + 2)^2 + 5

=> y = x^2 + 4x + 9

The standard form of the quadratic function with vertex (-2, 5) and passing through (0, 9) is y = x^2 + 4x + 9