Factorise fully y=x^2+x-12 and hence find the roots of the curve

To factorise a quadratic in the form ax^2+bx+c we need to find 2 numbers which add to get b and multiply to get c. In this case a=1, b=1 and c=-12. Two numbers which add to 1 and multiply to -12 are 4 and -3, so we can factorise this equation into two brackets: (x-3)(x+4). To check we are correct we can re-expand the brackets using the FOIL method (first, outer, inner, last), hence giving us x^2+4x-3x-12, which simplifies to... x^2+x-12. Now we can find the roots of the curve (the points at which the curve crosses the x-axis). These points are where y=0, so we sub this value into our equation: (x-3)(x+4)=0. We can now split the equation into its two brackets as anything multiplied by 0 is 0. Therefore x-3=0 and x+4=0, therefore the points at which this curve crosses the x-axis are x=3 and x=-4.