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

Oct 13, 2016

Standard form: $\textcolor{g r e e n}{f \left(x\right) = - {x}^{2} - 4 x + 5}$

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 $5 {x}^{\textcolor{red}{0}}$) has degree $\textcolor{red}{0}$
$- 4 x$ (which is equivalent to $- 4 {x}^{\textcolor{red}{1}}$has degree $\textcolor{red}{1}$
$- {x}^{\textcolor{red}{2}}$ has degree $\textcolor{red}{2}$

Depending upon your instructor, you may be required to make the coefficient of the $- {x}^{2}$ term explicit as
$f \left(x\right) = - \textcolor{m a \ge n t a}{1} {x}^{2} - 4 x + 5$