Question

How can I write { y=-x^2 - 2x in the form of y=a(x-h)^2+k by completing the square , deducing the coordinates of its vertex , writing down the equation of its axis of symmetry and finding its x-intercept } can somebody plz explain step by step ' plz help . :)

Answer 1

To understand completing the square you start with (x+c)^2 where c is just some constant (we are looking at this completely generally). If we expand this we get (x+c)(x+c) which equals x^2 + 2xc + c^2. If we look at your example you can see you have -(x^2 + 2x) and comparing that with the general example you can see that c must equal 1. Using this to write your example in in the form y = a(x-h)^2+k you should now be able to see that a and h are both -1 giving -(x+1)^2. To find k we notice that out of the general example you got the term c^2 and that doesn't exist in -x^2 -2x so you need to get rid of it. Out of -(x+1)^2 is going to pop -x^2 -2x -1 so in order to get rid of the minus one, k is going to need to be +1. Thus giving you -(x+1)^+1 where a=-1, h=-1 and k =1. Hope that helps, the rest is fairly straight forward.

Answer 2

Thankyou