The line y = 3x-4 intersects the curve y = x^2 - a, where a is an unknown constant number. Find all possible values of a.

For the line and the curve to intersect we need the for the following system of equations to have a solution. y = 3x AND y = x2 - aThe solution of the system of equations is found by solving x^2 - 3x - a = 0. (Interested in real numbers only)The solutions of a quadratic equation of the form ax^2 + bx + c = 0 can be obtained via the formula (-b +- sqrt(b^2 - 4ac) ) / (2a).The formula results in a valid (/real) value only when b^2 - 4ac >=0, which in our case is equivalent to 9 + 4a >= 0.As we are given that the two curve intersect, we must have 9 + 4a >= 0, and thus a can be any value greater or equal to -9/4.

Related Further Mathematics GCSE answers

All answers ▸

How would you differentiate x^x?


GCSE or A-level Maths: How can I find the x and y intercepts of a cubic function?


Factorise 6x^2 + 7x + 2


Find the coordinates of any stationary points of the curve y(x)=x^3-3x^2+3x+2


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