Finding the intersection of a two lines (curved and linear example)
Line 1: y = 2x + 2 Line 2: y = x2 - 1Firstly, intersection of two lines is the point at where the coordinates of both lines are the same. X1 = X2 and Y1 = Y2Therefore, that means we can exploit that fact and to find the point of intersection of line 1 substituting y of line 2 into line 1 ending up with: 2x + 2 = x2 -1We then need to rearrange so that it is in the normal format of a quadratic equation Ax2 + Bx + C = 0 x2 - 2x -3 = 0This means we can now take our normal approach of solving a quadratic equation by factoring. As the value of A is 1 it is a little bit simpler and we can use a trick of a+b = B and a*b = C to find our factors. (x - 3)(x + 1) = 0 therefore, x = 3 or x = -1substituting back into our simplest equation results in us finding the corresponding values of y. @ x = 3 y = 2(3) + 2 = 8 (3,8) @ x = -1 y = 2(-1) + 2 = 0 (-1,0)
