Write in Standard Form -2(x-4)^2+1

$- 2 {(x - 4)}^{2} + 1$

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

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

Simplify each term.

Rewrite ${(x - 4)}^{2}$ as $(x - 4) (x - 4)$ .

$- 2 ((x - 4) (x - 4)) + 1$

Expand $(x - 4) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$- 2 (x (x - 4) - 4 (x - 4)) + 1$

Apply the distributive property.

$- 2 (x \cdot x + x \cdot - 4 - 4 (x - 4)) + 1$

Apply the distributive property.

$- 2 (x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4) + 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$- 2 (x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4) + 1$

Move $- 4$ to the left of $x$ .

$- 2 (x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4) + 1$

Multiply $- 4$ by $- 4$ .

$- 2 (x^{2} - 4 x - 4 x + 16) + 1$

Subtract $4 x$ from $- 4 x$ .

$- 2 (x^{2} - 8 x + 16) + 1$

Apply the distributive property.

$- 2 x^{2} - 2 (- 8 x) - 2 \cdot 16 + 1$

Simplify.

Multiply $- 8$ by $- 2$ .

$- 2 x^{2} + 16 x - 2 \cdot 16 + 1$

Multiply $- 2$ by $16$ .

$- 2 x^{2} + 16 x - 32 + 1$

Add $- 32$ and $1$ .

$- 2 x^{2} + 16 x - 31$