Express x^2+4x-12 in the form (x+a)^2 +b by completing the square.
Completing the square of a function is sometimes used to find the stationary points on a curve, and also to solve when equaling zero. To complete the square firstly we have to halve the middle value of the parabola, this would be a, and put into brackets such that (x+a)2. For example with our given function, half of 4 is 2, and therefore the start of our completing the square would be (x+2)2. However if we expand this out we will not get the same result as x2+4x-12, and therefore we need to do a bit more work. If we expand it out we get x2+4x+4. However we want -12 instead of +4 as our constant. To achieve this we need to subtract the +4 and add the -12. This works for any example such that the constant is equal to (-a2 -c) with c being the constant of the original function. Therefore our answer works out to be (x+2)2-4-12 = (x+2)2-16. We can always check our answers by expanding the completed square and checking if it is equal to our original equation.
