Look at the graph of this system of equations: y = - x2 + 1 and y = x2. at which approximate points are the two equations equal?

Hey there!

Since you didn't provide your graph, I graphed it myself. I attached a picture just to make sure we're looking at the same thing. 

The points of intersection will be the solutions to a system of equation. There can be one solution or more than one. My next two attachments look at the two points of intersection closer so you can get a closer estimation. 

As you can see, on the x axis, the point (I'm talking about the one in my middle attachment on the negative side of the x-axis) is between –0.70 and –0.72 and is a little closer –0.70. This is a little less than –0.71. On the y-axis, you can see that the point is between 0.48 and 0.50, but pretty much goes through line 0.50. So, I would say this is about:

(–0.708, 0.50)

For the other point, it is symmetrical to this point, except the x-axis value will be positive. So, it's probably:

(0.708, 0.50)

I would say your answer is (–0.708, 0.50), (0.708, 0.50). Usually, for these estimation problems, if you get close enough to the actual answer your teacher will not mark you off. They'll probably only mark you off if you get it completely wrong, like if you said one of the points was at (0.8, 0.6) or something. 

Hope this helped you out! :-)