Formula for quadratic function with vertex (h, k) is:

f(x) = a(x - h)² + k

in our case h = 3, k = -4 thus we have

f(x) = a(x - 3) + (-4)

f(x) = a(x - 3) - 4

the graph of the function passes through (2, - 1):

f(2) = -1 or

a(2 - 3) - 4 = -1

by solving we find for a:

a = -3

click here to see the step by step solution of the equation:

the quadratic function is:

f(x) = (-3)(x - 3) - 4

f(x) = -3x + 9 - 4

f(x) = -3x + 5.