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 = -3x - 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 - 2y = 9 - 2y = 7
So one point of intersection is (-3, 7).
When x = 1:y = (1)^2 - 2y = 1 - 2y = -1
So the other point of intersection is (1, -1).
Therefore, the two equations intersect at (-3, 7) and (1, -1).
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).