Question

A) Show that x² - 8x + 20 can be written in the form (x - a)² + a where a is an integer.

b) Hence explain how you know that x² - 8x + 20 is always positive.

I have worked out the first bit of the question and the answer is:
x²-8x+20
x²-8x+16-16+20
(x-4)²+4
(x-a)²+a
a= 4

I just need help with part b and I'm struggling to do it. Please help.

Answer 1

Explanation:

b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.

You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive

Answer 2

b) x^2 - 8x + 20 is always positive because in part a, you figured out that it could also be written as (x-4)^2 + 4.
You know that (x-4)^2 is greater than or equal to 0 so by adding 4, the result will always be positive.