Express 9x^2-12x+5 into form (ax+b)^2+c

Answer 1

We have a trinomial 9x² – 12x + 5 . To write it in a vertex form , we need to recall the formula of square of the difference of two numbers. If you have two numbers a and b, then

                                                                  (a – b)² = a² – 2ab + b²

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In our case we have the highest order term 9x² . The square root of it is 3x. Then we have 12x. If we divide this term by 2, we will get 6x. We have already 3x. The coefficient near x is 3. Hence dividing 6 by 3, we will have 2. It means that our expression is

                                                                                   3x – 2.

Let us square it . We will obtain:

                                                                   (3x – 2)² = 9x² – 12x + 4.

Our given trinomial is 9x² – 12x + 5 could be represented as 9x² – 12x + 4 + 1. We finally see that

                                                               9x² – 12x + 5 = (3x – 2)²  + 1.

And this is the answer!