How many more unit tiles must be added to the function f(x)=x2-6x+1 in order to complete the square? T Oo oo BETEREN ER 00 WEEEEEE SEPTEMBER

Question

asked Jan 18, 2021 165k views

1 Answer

Scott Alan Miller · Answer 1 · 2021-01-22T11:20:40+0000

Answer:

It is necessary to sum 8 units

Explanation:

you have the following polynomial:

f(x)=x^2-6x+1 (1)

To complete the square you take into account the following general notable product:

(a-b)^2=a^2-2ab+b^2

Next, you take into account the coefficient of the second term in (1)

-6x = -2ab

a = x

-6a = -2ab

b = 6/2 = 3

Then, the third term must be:

b^2 = 3^2 = 9

But you have +1. Hence, you must sum 8, and also rest 8 in (1):

$f(x)=x^2-6x+(1+8)-8\\\\f(x)=(x^2-6x+9)-8\\\\f(x)=(x-3)^2-8$