How do you check if a graph ever touches the x-axis?

At the x-axis, y is always zero at any point. If you want to fnd out whether or not a graph reaches the x-axis, then substitute y=0 into the equation and find the value of x. If it solves, then we know it does touch the x-axis.

E.g. say we have an equation of y = 2x2-6x+4. Substituting y for 0 gives 2x2-6x+4=0. Factorising gives (2x-2)(x-2)=0, so x = 2 or 1. We know here that it touches the axis twice as we have two solutions.

Conversely, if we had y = x2+4, then substituting y for 0 gives x2+4=0 and therefore x = SquareRoot(-4). As we know, squareroots of negatives is not possible so x has no solutions, which means that this graph does not touch the x-axis.

Answered by Jawad C. Maths tutor

13012 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How can you expand brackets? e.g: (x-4)(x+7)


Solve the following for X and Y: 2y+4x=14 and x-y=-1


For the following right angled triangle find the value of x to 1 dp.


Amber earns £7 for each hour she works from Monday to Friday. She earns £10 for each hour she works on Saturday. One week Amber worked for 4 hours on Saturday. That week she earned a total of £180 (a) How many hours did Amber work that week?


We're here to help

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