A) show that x^2-8x+20 can be written in the form (x-a)^2+a where a is an integer
b) hence explain how you know that x^2-8x+20 is always positive

The equation in the form is

Given the quadratic function

We are to write this quadratic function in vertex form as shown:

Group the given expression

Hence the equation in the form is

Learn more on vertex form here: link

a)

Completing the square

b)

You can prove that is always positive, stating;

The sum of two squared numbers can't be negative. Hence is always positive.

Also, if we take the discriminant of

Once the discriminant is negative, the quadratic has no real root. So, the function never touches the real axis and the function lies above or below the real axis. If we take x as 0, y = 20, therefore, the function lies above the real axis. It is always positive.

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step-by-step explanation: