Find the coordinates where the curve f(X)= X^2+X-6 touches the x axis using factorisation.

The first part of this question requires be student to realise that touching the x axis equates to f(x) equalling 0, so we must equate the expression to 0.

Next we need to factorise the expression. This means we trying to find two numbers, a and b, which can be used to express the function in the form f(X)=(x-a)(x-b). If we multiply out this expression we see f(X)= X^2-(a+b)X+ab, so we need a+b=1 and ab=-6. Is we solve these simultaneously we find a=-3 b=2. If x=a or b we see one of the brackets equals 0 and since any number multiplied by 0 equals 0, So f(x) equals 0 (touches the x axis) when x= a or b.

WT
Answered by William T. Maths tutor

2924 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equations: 2x-3y = 16 x+2y= -6


Solve the following equation: 4x + 7 = 2x - 5


Factorise the quadratic equation: x^2 + 5x + 6 = 0 and hence find the two solutions to the equation.


Prove that the square of an odd number is always 1 more than a multiple of 4


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning