Write in Standard Form y=3(x+2)^2-1/2

$y = 3 {(x + 2)}^{2} - \frac{1}{2}$

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

Simplify each term.

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

$y = 3 ((x + 2) (x + 2)) - \frac{1}{2}$

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

Apply the distributive property.

$y = 3 (x (x + 2) + 2 (x + 2)) - \frac{1}{2}$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot 2 + 2 (x + 2)) - \frac{1}{2}$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) - \frac{1}{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 3 (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) - \frac{1}{2}$

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

$y = 3 (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) - \frac{1}{2}$

Multiply $2$ by $2$ .

$y = 3 (x^{2} + 2 x + 2 x + 4) - \frac{1}{2}$

Add $2 x$ and $2 x$ .

$y = 3 (x^{2} + 4 x + 4) - \frac{1}{2}$

Apply the distributive property.

$y = 3 x^{2} + 3 (4 x) + 3 \cdot 4 - \frac{1}{2}$

Simplify.

Multiply $4$ by $3$ .

$y = 3 x^{2} + 12 x + 3 \cdot 4 - \frac{1}{2}$

Multiply $3$ by $4$ .

$y = 3 x^{2} + 12 x + 12 - \frac{1}{2}$

Step 3

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = 3 x^{2} + 12 x + 12 \cdot \frac{2}{2} - \frac{1}{2}$

Step 4

Combine $12$ and $\frac{2}{2}$ .

$y = 3 x^{2} + 12 x + \frac{12 \cdot 2}{2} - \frac{1}{2}$

Step 5

Combine the numerators over the common denominator.

$y = 3 x^{2} + 12 x + \frac{12 \cdot 2 - 1}{2}$

Step 6

Simplify the numerator.

Multiply $12$ by $2$ .

$y = 3 x^{2} + 12 x + \frac{24 - 1}{2}$

Subtract $1$ from $24$ .

$y = 3 x^{2} + 12 x + \frac{23}{2}$

Step 7

Write in Standard Form y=3(x+2)^2-1/2

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