Question

How do you write this quadratic equation `f(x)=5-4x-x^2` in standard form?

Answer 1

Standard form: `color(green)(f(x)=-x^2-4x+5)`

Explanation:

Standard form for a polynomial requires that the terms be arranged in order of decreasing degree (where the degree of a term is the sum of the exponents of all variables in the term).

`5` (which is equivalent to `5x^color(red)(0)`) has degree `color(red)(0)`
`-4x` (which is equivalent to `-4x^color(red)1`has degree `color(red)1`
`-x^color(red)2` has degree `color(red)2`

Depending upon your instructor, you may be required to make the coefficient of the `-x^2` term explicit as
`f(x)=-color(magenta)1x^2-4x+5`