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

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

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

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

Simplify each term.

Rewrite ${(x - 9)}^{2}$ as $(x - 9) (x - 9)$ .

$y = (x - 9) (x - 9) + 2 x$

Expand $(x - 9) (x - 9)$ using the FOIL Method.

Apply the distributive property.

$y = x (x - 9) - 9 (x - 9) + 2 x$

Apply the distributive property.

$y = x \cdot x + x \cdot - 9 - 9 (x - 9) + 2 x$

Apply the distributive property.

$y = x \cdot x + x \cdot - 9 - 9 x - 9 \cdot - 9 + 2 x$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 9 - 9 x - 9 \cdot - 9 + 2 x$

Move $- 9$ to the left of $x$ .

$y = x^{2} - 9 \cdot x - 9 x - 9 \cdot - 9 + 2 x$

Multiply $- 9$ by $- 9$ .

$y = x^{2} - 9 x - 9 x + 81 + 2 x$

Subtract $9 x$ from $- 9 x$ .

$y = x^{2} - 18 x + 81 + 2 x$

Add $- 18 x$ and $2 x$ .

$y = x^{2} - 16 x + 81$