Write in Standard Form f(x)=(x-2)^2+6

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

Simplify each term.

Rewrite ${(x - 2)}^{2}$ as $(x - 2) (x - 2)$ .

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

Expand $(x - 2) (x - 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$f (x) = x \cdot x + x \cdot - 2 - 2 (x - 2) + 6$

Apply the distributive property.

$f (x) = x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2 + 6$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x) = x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2 + 6$

Move $- 2$ to the left of $x$ .

$f (x) = x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2 + 6$

Multiply $- 2$ by $- 2$ .

$f (x) = x^{2} - 2 x - 2 x + 4 + 6$

Subtract $2 x$ from $- 2 x$ .

$f (x) = x^{2} - 4 x + 4 + 6$

Step 3

Add $4$ and $6$ .

$f (x) = x^{2} - 4 x + 10$