Alan

1⁴ + (2-1)⁴ = 2  

2⁴ + (2-2)⁴ = 16

Solutions obtained as follows:

See https://web2.0calc.com/questions/please-help-asap-polynomial-division

Find the solutions to 16^x - 25*4^x + 24 = 0.

Let  u = 4^x, so the equation becomes:

u^2 -25u +24 = 0 This factorises as  (u - 24)(u - 1) = 0  so u = 24 and u = 1

Hence we have 4^x = 24    and  4^x = 1

Can you take it from here?   (Think about taking logs of both sides)

Just look at the term 5(x - 1/2)^2  (x-1)^2   

What happens to this term if you plug in x = 1/2?

What happens to it if you plug in x = 1?

"Your battery is not draining evenly. In the first hour it drained 19%. But, in the next 3 hours it drained 81% - 24% =57% ." !!!!

57% in 3 hours is 19% per hour.

For f(x) to equal 5 the term 5(x - 1/2)^2  (x-1)^2 must be zero.  Look carefully at this term.  What two values of x will make it zero?

As follows:

For question 2, the vertical asymptotes will occur where the denominator is zero.  These will be where the roots of the denominator are. i.e. they will be such that (x + 2)(x - 1) = 0

Expand this and compare with x^2 + ax + b =0,  to find a and b.

This graph should help with question 1: