Answer:
As written, the function is linear. If you meant f(x) = 4(x - 2)^2 + 3, then it opens upwards.
Explanation:
The key to find out whether a parabola opens upwards or downwards is the coefficient, or number in front, of the x^2 term. If the coefficient is positive, the parabola opens upward. If the coefficient is negative, the parabola opens downwards.
When simplifying f(x), squaring the inside using FOIL gives:
f(x) = 4(x^2 - 4x + 4) + 3
f(x) = 4x^2 - 16x + 16 + 3
Since the coefficient of x^2 is positive (4), the parabola opens upwards.