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# Draw the graphs of the functions and points of intersection for x^2 -2 and 2x^2 + 4x + 1

Let and . Find the points of intersection and draw the graph.

The points of intersection are at, Thus, they intersect at and . These correspond to the points and . The graph is below. 1. Anonymous says:

Hello! I believe the first intersection point is wrong, it should be (7, 7), or at least that’s what I get. I could be wrong too. Thanks for the solutions!

• RoRi says:

I think the points above are right. You can check by substituting in the values to see if the curves intersect there. So, for we have So, the graphs of and don’t go through the point (so definitely don’t intersect there).

The points we get above are and . We can check those: and So, it checks out, the graphs of both functions go through the points and they also both go through . Unless I copied the problem from the book wrong or something. (Which has been known to happen, and I don’t have my copy with me.)

• Anonymous says:

Yes, you are correct, I found my mistake substituting the values as they are. Thanks for the explanation!