Write in Standard Form y=-(x-1)^2-1

$y = - {(x - 1)}^{2} - 1$

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

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$y = - ((x - 1) (x - 1)) - 1$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$y = - (x (x - 1) - 1 (x - 1)) - 1$

Apply the distributive property.

$y = - (x \cdot x + x \cdot - 1 - 1 (x - 1)) - 1$

Apply the distributive property.

$y = - (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

$y = - (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) - 1$

Rewrite $- 1 x$ as $- x$ .

$y = - (x^{2} - x - 1 x - 1 \cdot - 1) - 1$

Rewrite $- 1 x$ as $- x$ .

$y = - (x^{2} - x - x - 1 \cdot - 1) - 1$

Multiply $- 1$ by $- 1$ .

$y = - (x^{2} - x - x + 1) - 1$

Subtract $x$ from $- x$ .

$y = - (x^{2} - 2 x + 1) - 1$

Apply the distributive property.

$y = - x^{2} - (- 2 x) - 1 \cdot 1 - 1$

Simplify.

Multiply $- 2$ by $- 1$ .

$y = - x^{2} + 2 x - 1 \cdot 1 - 1$

Multiply $- 1$ by $1$ .

$y = - x^{2} + 2 x - 1 - 1$

Step 3

Subtract $1$ from $- 1$ .

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

Step 4