Find the two points of intersection of the graphs y=x2 and y=x+2.

We know the presence of the quadratic means there must be two solutions for x. We can solve this problem by treating the formulas for the graphs as simultaneous equations. We can substitute in the formula for y into the equation involving the quadratic to eliminate the unknown y so we can solve for x. This yields the equation x+2=x2. We need to rearrange this equation so that all numbers are on one side. This makes solving the equation using the quadratic equation or factoring much easier. This gives us x2-x-2=0. We can now factor out this equation by finding the factors of -2 which add to make -1. This gives (x-2)(x+1)=0. For this equation to be true, x=2 and x=-1. We can now substitute these values of x into either equation to get the corresponding y value. This gives the two points of intersection to be (2,4) and (-1,1).

Answered by Sareena H. Maths tutor

6692 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

simplify c^4 x c^3


Write √ 45 in the form a √ 5, where a is an integer.


Tommy, Anna and Jacob all have 40 sweets. they decide to split the sweets between each other in the ratio 1:4:5. Calculate how many sweets each get, rounding down your answer where necessary.


What is rationalising a fraction?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences