Write in Standard Form y=(x-5)^2+16

$y = {(x - 5)}^{2} + 16$

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

$y = (x - 5) (x - 5) + 16$

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

Apply the distributive property.

$y = x (x - 5) - 5 (x - 5) + 16$

Apply the distributive property.

$y = x \cdot x + x \cdot - 5 - 5 (x - 5) + 16$

Apply the distributive property.

$y = x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5 + 16$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5 + 16$

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

$y = x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5 + 16$

Multiply $- 5$ by $- 5$ .

$y = x^{2} - 5 x - 5 x + 25 + 16$

Subtract $5 x$ from $- 5 x$ .

$y = x^{2} - 10 x + 25 + 16$

Step 3

Add $25$ and $16$ .

$y = x^{2} - 10 x + 41$

Step 4