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)

FF
Answered by Fabio F. Maths tutor

2744 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

One of the teachers at a school is chosen at random. The probability that this teacher is female is 3/5. There are 36 male teachers at the school. Work out the total number of teachers at the school.


N = 2a + b. a is a 2 digit square number, b is a 2 digit cube number. What is the smallest possible value of N?


Consider a right-angled triangle with an inside angle of 30° and a hypotenuse of 8cm. Calculate the length of the opposite side to the 30° angle.


Find the point(s) of intersection of the curve y=x^2+7x+14 and y=2x+8:


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences