Precalc
posted by Amy on .
use completing the square to describe the graph of each function.
How do you complete the square with this equations. please show me step by step so that I can understand it.
x^24x+6

x^2  4x + 6
first, yo only focus on the first two terms: x^2 and 4x. let's put a parenthesis to enclose them:
(x^2  4x) + 6
now, to complete the square, what we do is get the half of b (b is the numerical coefficient of x, and in this case, is 4) and we square it: (4/2)^2 = 4. Then we add a term +4 inside the parenthesis, but to remain the value of the whole expression constant, we also put a 4 but outside the parenthesis:
(x^2  4x + 4) + 6  4
the term inside the parenthesis is a perfect square, and we can further simplify this into:
(x2)^2 + 2
hope this helps~ :)