Find the Standard Form of the Function Equation: Rewrite f(x) = (-x+1)²+3

Find the standard representation of the following function

$f(x)=(-x+1)^2+3$

To convert the function $f(x) = (-x + 1)^2 + 3$ to its standard form, follow these steps:

Step 1: Expand the binomial $(-x + 1)^2$.
$(-x + 1)^2 = (-x)^2 + 2(-x)(1) + 1^2$

This simplifies to:
$(-x)^2 = x^2$
$2(-x)(1) = -2x$
$1^2 = 1$

Combining these terms gives:
$(-x + 1)^2 = x^2 - 2x + 1$

Step 2: Add the constant term $+3$ to the expanded form:
$f(x) = (x^2 - 2x + 1) + 3$

Step 3: Simplify the expression:
$f(x) = x^2 - 2x + 1 + 3 = x^2 - 2x + 4$

Thus, the standard representation of the function is $f(x) = x^2 - 2x + 4$.