Quadratic functions

Question

determine the standard form quadratic function, given the following: Vertex (4,-2), and passing through the point (1,1)

Answer 1

f(x) = a(x - 4)² - 2. To get a we use point (1, 1): f(1) = 1; a(1 - 4)² - 2 = 1; 9a = 3; a = 1/3

f(x) = 1/3(x - 4)² - 2; f(x) = 1/3x² - 8/3x + 10/3