SOLUTION: There is a graphic of the function y=2x+1 (line) and a graphic of the function y=x2-2 (parabola). Find out the points of intersection of the two functions. Draw the graphics and sh

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Question 1058499: There is a graphic of the function y=2x+1 (line) and a graphic of the function y=x2-2 (parabola). Find out the points of intersection of the two functions. Draw the graphics and show your calculations.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B1=x%5E2-2

Solve for x, and evaluate the corresponding y values.

graph%28350%2C350%2C-5%2C5%2C-3%2C7%2C2x%2B1%2Cx%5E2-2%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +y+=+2x+%2B+1+
(2) +y+=+x%5E2+-+2+
----------------------
Subtract (1) from (2)
(2) +y+=+x%5E2+-+2+
(1) +-y+=+-2x+-+1+
-----------------------
+0+=+x%5E2+-+2x+-+3+
+%28+x+-+3+%29%2A%28+x+%2B+1+%29+=+0+ ( by inspection )
--------------------------
+x+=+3+ and +x+=+-1+
are the solutions
--------------------------
Plug both solutions into either (1) or (2)
+x+=+3+
(1) +y+=+2%2A3+%2B+1+
(1) +y+=+7+
One intersection is ( 3, 7 )
----------------------------
+x+=+-1+
(1) +y+=+2%2A%28-1%29+%2B+1+
(1) +y+=+-1+
2nd intersection is ( -1, -1 )
-----------------------------
Here's the plot:
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+10%2C+2x+%2B+1%2C+x%5E2+-+2+%29+
My solutions look OK