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Need help finding the intersecting points between curves?
So, basically, I'm trying to find the intersection points between curves. I get the gist of how to do it: You set them equal, get one side to zero, then factor, you have your two roots. But when I do it, all of my answers are unfactorable.
Example, for y = x^2-2x+8 and y = x+6
I set them equal
x^2-2x+8 = x+6
then set one side to 0
x^2-3x+14 = 0
And then... oh, this is unfactorable.
But then if I put them into a graph, I can see they intersect at 1 and 2. What am I doing wrong? That was the first question from my homework, so I think it should be doable.
Thanks in advance
HAHAHA! Don't I feel stupid. Thanks you guys. That was how I would have factored it too.
4 Answers
- RATTYLv 79 years ago
The curve y = x^2 - 2x + 8 intersects with the line y = x+6 when:
x^2 - 2x + 8 = x + 6
=> x^2 - 3x + 2 = 0 This is where you have gone wrong. We are subtracting 6 from both sides.
Now solve this quadratic for x by factorising:
=> x^2 -2x - x + 2 = 0
=> x(x - 2) - 1(x - 2) = 0
=> (x - 2)(x -1) = 0
=> x = 2 or x = 1
When x = 2, y = 2 + 6 = 8
When x = 1, y = 1 + 6 = 7
Answer: the intersecting points of the curves are (2,8) and (1,7)
- RaffaeleLv 79 years ago
I set them equal
x^2-2x+8 = x+6 <--- x^2 - 2 x + 8 - x - 6 = 0
then set one side to 0
x^2-3x+14 = 0 <--- it's wrong: should be x^2 - 3x + 2 = 0
