To find where these two functions intersect, we can set them equal to each other and solve for x:

x^2 - 4x + 4 = 4 - x^2

Adding x^2 to both sides:

2x^2 - 4x + 4 = 4

Subtracting 4 from both sides:

2x^2 - 4x = 0

Factoring out a common factor of 2x:

2x(x - 2) = 0

Setting each factor equal to zero:

2x = 0 or x - 2 = 0

x = 0 or x = 2

So the two functions intersect at x = 0 and x = 2.

To find the corresponding y-values, we can plug these values back into either of the original functions.

For x = 0:

y = 0^2 - 4(0) = 0
y = 4 - 0^2 = 4

So the point of intersection at x = 0 is (0, 4).

For x = 2:

y = 2^2 - 4(2) = 4 - 8 = -4
y = 4 - 2^2 = 4 - 4 = 0

So the point of intersection at x = 2 is (2, -4).

Therefore, the two functions intersect at the points (0, 4) and (2, -4).