The problem requires us to find the points of intersection of the two given curves: $y = x^2$ and $y = -x^2 + 2$.

1. Problem Description

The problem requires us to find the points of intersection of the two given curves: $y = x^2$ and $y = -x^2 + 2$.

2. Solution Steps

To find the points of intersection, we need to solve the system of equations:

$y = x^2$

$y = -x^2 + 2$

Since both equations are equal to $y$, we can set them equal to each other:

$x^2 = -x^2 + 2$

Add $x^2$ to both sides:

$2x^2 = 2$

Divide both sides by 2:

$x^2 = 1$

Take the square root of both sides:

$x = \pm 1$

Now we can find the corresponding $y$ values for each $x$ value using the equation $y = x^2$:

If $x = 1$, then $y = (1)^2 = 1$.

If $x = -1$, then $y = (-1)^2 = 1$.

Thus, the intersection points are $(1, 1)$ and $(-1, 1)$.

3. Final Answer

The points of intersection are $(1, 1)$ and $(-1, 1)$.