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

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

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Answer 1 · 2016-10-13T10:40:25

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

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).

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

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

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

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Explanation:

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