Point of intersection

tigs

New member
Joined
Feb 28, 2019
Messages
2
Find the coordinates of the points of intersection of the line with equation y=x+k and the parabola with equation y=2x+x2, where k>0.

I tried doing x+k=2x+x2, which then become k=x+x2, but don't know where to go from there ...
 

Romsek

Full Member
Joined
Nov 16, 2013
Messages
251
\(\displaystyle x^2+x-k=0\)

apply the quadratic formula
 

tigs

New member
Joined
Feb 28, 2019
Messages
2
\(\displaystyle x^2+x-k=0\)

apply the quadratic formula
Are the x values I get after applying the quadratic formula, the x values of the coordinates of the points of intersection? To get the y values, do I put those x values into the equation y=x+k or y=2x+x2? Won't that give me four different coordinates when there should be only two?
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,375
Your equation says that the y values on the two curves for a given x are equal -- so, yes, its solutions are the x-coordinates of the (two) intersections.

For each such solution, you can plug it into either of the original equations to find the corresponding y. You will get the same value of y from each equation (assuming you solved correctly), because that's what your equation says will happen. Did you try doing that? You won't get four points, just two.

The general formula is a little complex, so you have to be careful plugging into the quadratic, but it's worth the experience.
 
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