What is the best way of differentiating intersection of two curves and touching of curves

 In this illustration we will utilize the bends y=2x2 , and y=x2+1. This is an exceptionally clear case, yet exhibits the strategy for finding the crossing point of two bends well. 

Step 1 - since the LHS of both these conditions is the same (y=...) we can liken the two conditions: 

2x2=x2+1 

This is a genuinely simple condition to illuminate: 

Lets make one side equivalent to zero: 

- x2 +1=0 

Lets move everything crosswise over to the opposite side to dispose of the less signs. 

x2 - 1 =0 

This is the distinction of two squares, so can be factorized: 

(x+1)(x-1)=0 

So the x-directions of the crossing point focuses are +1 and - 1. 

Step 2 - Now we have to discover the y-facilitates. We do this by connecting the x-qualities to the first conditions. We can utilize it is possible that one, in light of the fact that the lines meet (so they ought to give us a similar outcome!) 

At the point when x= +1, 

y=2x2 

y=2(1)2 =2 

At the point when x= - 1 

y=2(- 1)2 = 2 

So the purposes of crossing point have facilitates (- 1,2) and (1,2) .