Question

the function f is defined by f(x)=x²-4x+8 for x∈R
(i) Express x²-4x in the form(x-a)²+b

Answer 1

Answer:

This is the form of (x-a)^2 +b is f(x) = (x-2)^2 +4

Step-by-step explanation:

Step 1:-

Given function f(x) = x^2 -4 x +8

$f(x) = x^{2} - 2 (2 x) +4 +4$

$f(x) = x^{2} -2(2 x) +(2)^2+4$

we will use formula

$(a-b)^{2} = a^{2} -2 a b+b^{2}$

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

this is the form of

$(x-a)^2+b$

Final answer:-

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