A curve has equation y = 4x^2 + 5x + 3. A line has equation y = x + 2. What is the value of x?

First you as both equations are = to y you can make them equal to eachother. 4x2 +5x +3 = x+ 2.Then you rearrange the equation to gather all the terms on one side and make the equation = to 0. You minus x from both sides and then minus 2 from both sides to give you :4x2+4x+1 = 0. Then there are two options.The slightly harder but more time efficient way is: you may want to divide each term by 4 to give 4(x2 +x +1/4) = 0 then divide both sides by 4 to give x2+x+1/4 = 0. Then find two numbers that add to make 1 and times to make a quarter, which you may be able to see is 1/2. So (x+1/2)2=0 and so x=-1/2.Or you may find it easier to put the values from the equation 4x2+4x+1 = 0 into the quadratic formula (write on whiteboard)to give x= - 1/2.

Answered by Katherine H. Maths tutor

5957 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Given the function f(x) = 2x^(2) + 3, find the value of x when f(x) = 53.


Expand 2a (4 + a)


(This was taken from a GCSE past paper)A bag of 24 spoons costs £19.95. A box of 18 forks costs £15.55. Bags and boxes cannot be split. Gregor decides to buy the same number of spoons as forks. He places an order to buy the smallest number of each


A and B are points on a circle, centre O. BC is a tangent to the circle. AOC is a straight line. Angle ABO = x°. Find the size of angle ACB, in terms of x. Give your answer in its simplest form. Give reasons for each stage of your working.


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