Question:
Finding the intersection of two lines (curved and linear example) Line 1: y = 2x + 2 Line 2: y = x^2 – 1.
Methods:
Firstly, intersection of two lines is the point at where the coordinates of both lines are the same. X1 = X2 and Y1 = Y2
Therefore, 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 = x^2 -1. We then need to rearrange so that it is in the normal format of a quadratic equation Ax^2 + Bx + C = 0 x^2 – 2x -3 = 0
This 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 = -1
Substituting back into our simplest equation results in us finding the corresponding values of y.
when x = 3 y = 2(3) + 2 = 8
when x = -1 y = 2(-1) + 2 = 0
Answer:
(3,8) (-1,0)
Need extra GCSE Maths Help?
Join our community of students 📝
Every year, 92% our students successfully boost their grades by 2 or more in their core subjects.
