Does the parabola
f(x) = 4(x - 2)2 + 3
open up or down?

As written, the function is linear. If you meant f(x) = 4(x - 2)^2 + 3, then it opens upwards.

Step-by-step 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.

the first one, all those points on the line just make a strait line.