Write in Standard Form y=-4(x+5)^2

$y = - 4 {(x + 5)}^{2}$

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 ${(x + 5)}^{2}$ as $(x + 5) (x + 5)$ .

$y = - 4 ((x + 5) (x + 5))$

Step 3

Expand $(x + 5) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$y = - 4 (x (x + 5) + 5 (x + 5))$

Apply the distributive property.

$y = - 4 (x \cdot x + x \cdot 5 + 5 (x + 5))$

Apply the distributive property.

$y = - 4 (x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5)$

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = - 4 (x^{2} + x \cdot 5 + 5 x + 5 \cdot 5)$

Move $5$ to the left of $x$ .

$y = - 4 (x^{2} + 5 \cdot x + 5 x + 5 \cdot 5)$

Multiply $5$ by $5$ .

$y = - 4 (x^{2} + 5 x + 5 x + 25)$

Add $5 x$ and $5 x$ .

$y = - 4 (x^{2} + 10 x + 25)$

Step 5

Apply the distributive property.

$y = - 4 x^{2} - 4 (10 x) - 4 \cdot 25$

Step 6

Simplify.

Multiply $10$ by $- 4$ .

$y = - 4 x^{2} - 40 x - 4 \cdot 25$

Multiply $- 4$ by $25$ .

$y = - 4 x^{2} - 40 x - 100$

Step 7