Question

Use the method of completing the square for F(x)=x^2 - 8x + C, to
determine the value of F(2)

Answer 1

`F(2)=C-12`

Explanation:

Given:
`F(x)=x^2-8x+C`

To find: value of
`F(2)`

Solution:

`F(x)=x^2 - 8x + C\\=x^2-2(4)x+C`

Add and subtract
`4^2` in the left side of the equation

`F(x)=x^2-2(4)x+4^2-4^2+C`

Use formula:
`(a-b)^2=a^2-2ab+b^2`

`F(x)=(x-4)^2-4^2+C\\=(x-4)^2+C-16`

Put
`x=2`

`F(x)=(x-4)^2+C-16\\F(2)=(2-4)^2+C-16\\=4+C-16\\=C-12`