Express (x-6)² + 2x in Standard Function Form

Question

Find the standard representation of the following function

$f(x)=(x-6)^2+2x$

To solve this problem, we'll transform the given expression into standard quadratic form by expanding and simplifying:

Step 1: Expand $(x - 6)^2$
$(x - 6)^2 = x^2 - 12x + 36$
Step 2: Add $2x$
$f(x) = x^2 - 12x + 36 + 2x$
Step 3: Simplify
Combine like terms: $-12x + 2x = -10x$ , resulting in the expression:
$f(x) = x^2 - 10x + 36$

Therefore, the standard form of the function $f(x)$ is $x^2 - 10x + 36$ . This corresponds to choice 1 in the given list.

Thus, the final solution is $f(x) = x^2 - 10x + 36$ .

$f(x)=x^2-10x+36$