Question

Find the values of a and b such that x^2-2x+2=(x-a)^2+b

Answer 1

Answer:

a = 1, b = 1

Step-by-step explanation:

Expand the right side and compare the coefficients of like terms on both sides, that is

right side

(x - a)² + b ← expand factor using FOIL

= x² - 2ax + a² + b

Compare to left side x² - 2x + 2

Compare the coefficients of the x- term

- 2a = - 2 ( divide both sides by - 2 )

a = 1

Compare the constant terms

a² + b = 2 ( substitute a = 1 )

1² + b = 2

1 + b = 2 ( subtract 1 from both sides )

b = 1

Thus a = 1, b = 1