Question

Does the line y=x intersect the parabola y=-x².If so, how many times and where? Draw graphs on the same set of axes.

Answer 1

Answer:

Yes, the line intersects the parabola two times at the points (0,0) and (-1,-1)

Step-by-step 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!