How can  I find the coordinates of crossing points between the line y=2x+1 and the curve y=x^2+x+1?

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neela's profile pic

Posted on

At the point of intersection, the ordinates of the two curves are equal .

So 2x+1 = x^2+x+1

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

x^2-x = 0

x(x-1) = 0

x=0 or x= 1.

When x=0 , from y =2x+1 , we get y = 2*0 +1 =1

When x=1, y =2*1 +1 =3


(0 ,1) and (1, 3)

giorgiana1976's profile pic

Posted on

The coordinates of the intercepting point have to verify both, the equation of the line and the equation of the curve.


We'll factorize:


We'll put each factor as 0:

 x=0 and x-1=0, x=1

Now, we'll substitute the x values in one of the 2 equation, and we'll do it in the linear equation,because it's more easy to calculate:



y=2*0+1, y=1

So the first intercepting point: A(0,1) 



So the second intercepting point: B(1,3).

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