Answer :
(x - 1)² + 4
a = -1
b = 4
Work.
Given the equation:
x² - 2x + 5
Rewrite in the form:
(x + a)² + b
This form is obtained by completing the square.
x² - 2x + 5
Halve b and square it.
-2/2 = -1
(-1)² = 1
Add and subtract it from the equation.
It becomes:
x² - 2x + 1 - 1 + 5
Group to make a trinomial and add like terms.
(x² - 2x + 1) + 4
Rewrite the trinomial as a square.
(x - 1)²
Add the constant.
Final product.
(x - 1)² + 4
