To find the point(s) of intersection between the two equations, we can set them equal to each other and solve for x:

x^2 - 2 = 1 - 2x

Adding 2x to both sides and subtracting 1 from both sides:

x^2 + 2x - 3 = 0

Now we can factor the quadratic equation:

(x + 3)(x - 1) = 0

Setting each factor to zero:

x + 3 = 0 --> x = -3
x - 1 = 0 --> x = 1

So the two equations intersect at x = -3 and x = 1.

To find the corresponding y-values, we can plug these x-values back into one of the original equations. Using y = x^2 - 2:

When x = -3:
y = (-3)^2 - 2
y = 9 - 2
y = 7

So one point of intersection is (-3, 7).

When x = 1:
y = (1)^2 - 2
y = 1 - 2
y = -1

So the other point of intersection is (1, -1).

Therefore, the two equations intersect at (-3, 7) and (1, -1).