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).

SH
Answered by Sareena H. Maths tutor

7276 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

There are n sweets in a bag. 6 are orange. A random sweet gets eaten, and then a second one. The probability that both sweets are orange is 1/3. Find n.


How many 4 digit numbers are such that the first digit is non-zero and it is overall a multiple of 5?


Solve the simultaneous equations 3x + y = –4 and 3x – 4y = 6


Write down the value of 36^0.5


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