Question

Hi Guys I'm stuck on this question

write x^2-4x+2 in the form (x-A)^2+B

Answer 1

(x-2)^2-2

Explanation:

x^2-4x+2

take the x out

x(x-4) + 2

(x-2)^2-2

because (x-2)^2 is

x^2-4x+4

its like completing the square

Answer 2

(x-2)² -2

Explanation:

Consider that (a+b)² = a²+2ab+b²

To find the form (x-A)²+B compare x²-4x+2 with a²+2ab+b²

x² - 4x +2

a² + 2 a b+ b², so a= x and b = (-2)

x²+ 2· x ·(-2)+ (-2)² - 2 = (x-2)² -2 is in the form (x-A)²+B

Check our answer:

(x-2)² -2= (x²-2·2x+4)-2 = x²-4x +2 ✅