y = x2 – 4; y = x – 2
To find the intersection points, we need to solve the system of equations:
y = x^2 - 4
y = x - 2
Since y is equal in both equations, we can set them equal to each other:
x^2 - 4 = x - 2
Now, we want to solve for x:
x^2 - x - 2 = 0
This is a quadratic equation, so we can try to factor it.
(x - 2)(x + 1) = 0
This gives us two possible solutions for x:
x - 2 = 0 => x = 2
x + 1 = 0 => x = -1
Now, we can plug these solutions back into either of the original equations to find the corresponding y values.
For x=2:
y = (2)^2 - 4
y = 4 - 4
y = 0
For x=-1:
y = (-1)^2 - 4
y = 1 - 4
y = -3
Thus, the intersection points of the two curves are:
(2, 0) and (-1, -3)