Answer:
f(x) = (x - 2)² - 1
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given
f(x) = x² - 4x + 3
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 4x
f(x) = x² + 2(- 2)x + 4 - 4 + 3
= (x - 2)² - 1
Answer:
f(x) = (x - 2)^2 - 1
Step-by-step explanation:
f(x) = x^2 - 4x + 3 is the proper way in which to write this; the " ^ " signifies "exponentiation," where x2 is meaningless.
To complete the square:
Rewrite f(x) = x^2 - 4x + 3 as f(x) = x^2 - 4x + 3
Take half of the coefficient of x (end result is -2), square this end result and add, then subtract, it from f(x) = x^2 - 4x:
f(x) = x^2 - 4x + (-2)^2 - (-2)^2 + 3, or
f(x) = x^2 - 4x + 4 - 4 + 3
Rewrite x^2 - 4x + 4 as the square of x - 2:
f(x) = (x - 2)^2 - 1
This is the equation in vertex form; the vertex is (2, -1).
