Okay so the first thing we can identify is that it is a quadratic, hence the x² at the beginning. From this we can now start to answer the question. To calculate the minimum point we must "complete the square"; this method involves getting the x into a squared bracket, so from "x²" to "(x+ or -...)² " whilst considering the number which is not a coefficient (the number made when the squared racket is multiplied out). The first thing we do is halve the x coefficient (so the 4x). In order to 'recreate' the 4x you would have to have two lots of the new coefficient, 2x. If this is put into a squared bracket like so: (x+2)², when multiplied out you have x²+4x (which is what you want) +4, which is what you want to change. The target equation is in the question, so in order for x²+4x +4 to become x²+4x -5, you have to subtract 9. As x²+4x+4 is equal to (x+2)², the equation x²+4x-5 is equal to (x+2)²-9. The minimum point is (-x coefficient, Number outside) so it would be (-2, -9).

Factorise X^2-X-20

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