SOLUTION: I have to identify and solve quadratic systems. i really don't get this at all. So, if you could help me solve the problem, it would be greatly appreciated. 1) y= x-2 y= x^2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I have to identify and solve quadratic systems. i really don't get this at all. So, if you could help me solve the problem, it would be greatly appreciated. 1) y= x-2 y= x^2      Log On


   



Question 28071: I have to identify and solve quadratic systems. i really don't get this at all. So, if you could help me solve the problem, it would be greatly appreciated.
1) y= x-2
y= x^2-2
or y= x-1
y=x^2
either one would be great. THANK YOU!!!

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
y=x-2 and y=x%5E2-2

Solving means where are they equal? How to do that? by putting them EQUAL! Sounds obvious, but that needs to be said, since you do not know how to solve this.

well, if y equal (x-2) and also y equal x%5E2-2, then surely x-2+=+x%5E2-2?

x-2+=+x%5E2-2
-2+=+x%5E2-x-2
0+=+x%5E2-x
just re-ordering... x%5E2-x+=+0
x(x-1) = 0

so either x=0 OR x-1=0
--> x=0 OR x=1

and when x=0, y=-2
and when x=1, y=-1

(0, -2) and (1, -1) are the 2 answers (the 2 points) that satisfy BOTH equations.

Graphically, we have a quadratic, u-shape and a straight line. The straight line cuts the u-shape twice and the coordinates i found are these two points.

the graph is...

graph%28300%2C300%2C-4%2C4%2C-6%2C6%2C+x-2%2C+x%5E2-2%29

jon.