Write in Standard Form f(x)=3(x-3)^2+9

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

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 $(x - 3) (x - 3)$ .

$f (x) = 3 ((x - 3) (x - 3)) + 9$

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

Apply the distributive property.

$f (x) = 3 (x (x - 3) - 3 (x - 3)) + 9$

Apply the distributive property.

$f (x) = 3 (x \cdot x + x \cdot - 3 - 3 (x - 3)) + 9$

Apply the distributive property.

$f (x) = 3 (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3) + 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 3$ by $- 3$ .

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

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

$f (x) = 3 (x^{2} - 6 x + 9) + 9$

Apply the distributive property.

$f (x) = 3 x^{2} + 3 (- 6 x) + 3 \cdot 9 + 9$

Simplify.

Multiply $- 6$ by $3$ .

$f (x) = 3 x^{2} - 18 x + 3 \cdot 9 + 9$

Multiply $3$ by $9$ .

$f (x) = 3 x^{2} - 18 x + 27 + 9$

Step 3

Add $27$ and $9$ .

$f (x) = 3 x^{2} - 18 x + 36$