Answer:
f(x) = (x - 2)²
Step-by-step explanation:
f(x) = x² - 4x + 4 is a perfect trinomial.
You know a trinomial is perfect when double the square root of the first term multiplied by the square root of the last term equals the middle term.
As an equation, a trinomial in the form ax² + bx + c = 0:
2√a√c = b is a perfect trinomial.
Perfect trinomial are factored in this form:
(√a ± √c )(√a ± √c ) = (√a ± √c )²
Whether the sign is + or - depends on if the middle term is positive or negative.
In f(x) = x²-4x+4, the middle term is a negative.
The square root of the first term is 1.
The square root of the second term is 2.
The factored form is (x - 2)²
