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

$y = {(x - 3)}^{2}$

Step 1

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

$y = a x^{2} + b x + c$

Step 2

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

$y = (x - 3) (x - 3)$

Step 3

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

Apply the distributive property.

$y = x (x - 3) - 3 (x - 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot - 3 - 3 (x - 3)$

Apply the distributive property.

$y = x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3$

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3$

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

$y = x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$y = x^{2} - 3 x - 3 x + 9$

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

$y = x^{2} - 6 x + 9$

Step 5