A graph is sketched with the equation x^2+4x-5. Find the minimum point of this graph.
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).
