Express the quadratic polynomial x²-4x+9 in completed square form with working so i can understand it. thanks.

Answer 1

Ok we have x^2-4x+9
thets remember the basic rules for completing the square
ax^2+bx+c
(ax+(b/2))^2+c=(b/2)^2
so
(x-2)^2+9=-4
so expressed in completing the square form gives us
(x-2)^2+5

Answer 2

x^2 + 4x + 9 = 0 pass the consistent over: x^2 + 4x = -9 Take the b-term, that's 4, split it in a million/2 to get 2, and sq. that to get 4. upload this to the two facets: x^2 + 4x + 4 = -5 discover the squared term: (x + 2)^2 = -5 Take the sq. roots: x + 2 = isqrt(5) and x + 2 = -isqrt(5) Subtract 2, and we are performed: x = isqrt(5) - 2 and x = -isqrt(5) - 2

Answer 3

remember that (a - b)^2 = a^2 - 2ab + b^2
Plug a=x, b=2 into it and get:
(x - 2)^2 = x^2 - 2*2x + 2^2 = x^2 - 4x + 4

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

add 9:

x^2 - 4x + 9 = (x - 2)^2 - 4 + 9 = (x - 2)^2 + 5

Answer 4

x^2-4x+9
=x^2-4x +4+5
=(x-2)^2+5 ANS.

Answer 5

Okay you have y=x^2-4x+9.
Now subtract 9 from both sides,
y-9=x^2-4x.
Now, add (4/2)^2 to both sides,
y-9+(4/2)^2=x^2-4x+(4/2)^2, or
y-9+4=x^2-4x+4, or
y-5=(x-2)^2, or y=(x-2)^2+5 and there you have it!

Answer 6

ADd and subtract (4 / 2) ² :-
(x ² - 4 x + 4) + (9 - 4)
(x - 2) ² + 5