Write in Standard Form y=3(x-4)^2-22

$y = 3 {(x - 4)}^{2} - 22$

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

$y = 3 ((x - 4) (x - 4)) - 22$

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

Apply the distributive property.

$y = 3 (x (x - 4) - 4 (x - 4)) - 22$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot - 4 - 4 (x - 4)) - 22$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4) - 22$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 3 (x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4) - 22$

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

$y = 3 (x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4) - 22$

Multiply $- 4$ by $- 4$ .

$y = 3 (x^{2} - 4 x - 4 x + 16) - 22$

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

$y = 3 (x^{2} - 8 x + 16) - 22$

Apply the distributive property.

$y = 3 x^{2} + 3 (- 8 x) + 3 \cdot 16 - 22$

Simplify.

Multiply $- 8$ by $3$ .

$y = 3 x^{2} - 24 x + 3 \cdot 16 - 22$

Multiply $3$ by $16$ .

$y = 3 x^{2} - 24 x + 48 - 22$

Step 3

Subtract $22$ from $48$ .

$y = 3 x^{2} - 24 x + 26$

Step 4