Problem:
find the sum of the constants a, b ,c and such that
2x^2-8x+7=a(x-h)^2+k
for all real numbers

3

Step-by-step explanation:

The problem is to complete the square on the quadratic expression 2x^2 - 8x + 7. First, we write

                                    2x^2 - 8x + 7 = 2(x^2 - 4x) + 7

We want a square that includes the terms x^2 and -4x. This desired square is

                                      (x - 2)^2 = x^2 - 4x + 4

Hence,

                                    2(x^2 - 4x) + 7 &= 2[(x^2 - 4x + 4) - 4] + 7  

                                        = 2[(x - 2)^2 - 4] + 7  

                                        = 2(x - 2)^2 - 8 + 7  

                                        = 2(x - 2)^2 - 1.

Therefore, a = 2, h = 2, and k = -1, and a+h+k = 3

step-by-step explanation: