Question

determine the quadratic function of f whose graph is the vertex of (1,-4) and the y-intercept is -3.

Answer 1

since we know the vertex,start with
y = a(x-1)^2 - 4

but (0,-3) lies on it , so ...
-3 = a(0-1)^2 - 4
-3+4 = a
a = 1

y = (x-1)^2 - 4