Write in Standard Form f(x)=(x-3)^2+2

$f (x) = {(x - 3)}^{2} + 2$

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 ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

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

Expand $(x - 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$f (x) = x \cdot x + x \cdot - 3 - 3 (x - 3) + 2$

Apply the distributive property.

$f (x) = x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 + 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x) = x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 + 2$

Move $- 3$ to the left of $x$ .

$f (x) = x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 + 2$

Multiply $- 3$ by $- 3$ .

$f (x) = x^{2} - 3 x - 3 x + 9 + 2$

Subtract $3 x$ from $- 3 x$ .

$f (x) = x^{2} - 6 x + 9 + 2$

Step 3

Add $9$ and $2$ .

$f (x) = x^{2} - 6 x + 11$