Question

I am confused on this transformation problem. Can anybody help?

Answer 1

The new function is `0.1607x^2-0.7557x+3.0525`

Explanation:

The fine function is `f(x)=0.1607x^2+1.8155x+7.2917`

Note that if `x=0`, fine is `7.2917`.

The function can be written as

`0.1607(x^2+1.8155/0.1607x)+7.2917`

= `0.1607(x^2+11.2974x)+7.2917`

= `0.1607(x^2+2xx5.6487x+(5.6487)^2)-0.1607xx(5.6487)^2+7.2917`

= `0.1607(x+5.6487)^2-5.1276+7.2917`

= `0.1607(x+5.6487)^2+2.1641`

Now creating a buffer of `8` means that if `x=8`, we should have fine `7.2917` instead of this being at `x=0`.

this will be at `0.1607(x+5.6487-8)^2+2.1641`

i.e. `0.1607(x-2.3513)^2+2.1641`

= `0.1607(x^2-4.7026x+5.5286)+2.1641`

= `0.1607x^2-0.7557x+0.8884+2.1641`

= `0.1607x^2-0.7557x+3.0525`