Answer:
Yes, the line intersects the parabola two times at the points (0,0) and (-1,-1)
Explanation:
Hi there!
We have the following system of equations:
y = x
y = -x²
If the curves intersect, then there is at least a pair (x,y) that satisfies both equations. That will only happen for those values of x for which:
-x² = x
The only two values that satisfy that equality are 0 and -1.
When x = 0, y is also 0 for both functions. In the same way, when x = -1 y is also -1 for both functions. Then, the curves will intersect at the points (0, 0) and (-1, -1).
Please, see the attached graphic for a better understandign of the problem.
Have a nice day!