Write in Standard Form y=6(x-2)^2-8

$y = 6 {(x - 2)}^{2} - 8$

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

$y = 6 ((x - 2) (x - 2)) - 8$

Expand $(x - 2) (x - 2)$ using the FOIL Method.

Apply the distributive property.

$y = 6 (x (x - 2) - 2 (x - 2)) - 8$

Apply the distributive property.

$y = 6 (x \cdot x + x \cdot - 2 - 2 (x - 2)) - 8$

Apply the distributive property.

$y = 6 (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2) - 8$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 6 (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2) - 8$

Move $- 2$ to the left of $x$ .

$y = 6 (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2) - 8$

Multiply $- 2$ by $- 2$ .

$y = 6 (x^{2} - 2 x - 2 x + 4) - 8$

Subtract $2 x$ from $- 2 x$ .

$y = 6 (x^{2} - 4 x + 4) - 8$

Apply the distributive property.

$y = 6 x^{2} + 6 (- 4 x) + 6 \cdot 4 - 8$

Simplify.

Multiply $- 4$ by $6$ .

$y = 6 x^{2} - 24 x + 6 \cdot 4 - 8$

Multiply $6$ by $4$ .

$y = 6 x^{2} - 24 x + 24 - 8$

Step 3

Subtract $8$ from $24$ .

$y = 6 x^{2} - 24 x + 16$

Step 4