Answer

Explanation
The standard form of a parabola is

where
, and
are real numbers.
If it passes through (0,3) then when x = 0, y = 3 so this means that

so
.
If it passes through (1,-4), then when x = 1, y = -4 so

If it passes through (-1,4) then when x = -1, y = 4 so

Because both (I) and (II) need to be satisfied, we have the system of equations,

which we can easily solve by adding the two equations up to get

Then we take any of the previous equations to solve for b:

Thus the parabola in standard form is
