Question

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

Answer 1

3

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

Answer 2

2(x-2)^2 +3. You ignore the 7 and complete the square for 2x^2 -8 and then subtract what you add from the 7