SOLUTION: find the coordinates of the points of intersection of the parabola y=x2 and the line y=x+2

Here is the graph of the parabola y=x²



Here is the graph of the line y=x+2:



Now we'll find the coordinates of those two points where
they intersect:



Substitute  for y in the second equation:



Get 0 on the right:



Factor the left side:



Use the zero factor principle:

x-2 = 0     x+1 = 0
  x = 2       x = -1

Now we have to find the y coordinates to go
with each of these x-coordinates:


Find the y-coordinate that goes with x = 2
by substituting in

y = x+2
y = 2+2
y = 4

So one point is (x,y) = (2,4)


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Find the y-coordinate that goes with x = -1
by substituting in

y = x+2
y = -1+2
y = 1

So the other point is (x,y) = (-1,1)

And if we look at the graph we see that it checks
with those:



Edwin