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

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

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 ${(x - \frac{2}{3})}^{2}$ as $(x - \frac{2}{3}) (x - \frac{2}{3})$ .

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

Expand $(x - \frac{2}{3}) (x - \frac{2}{3})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Combine $x$ and $\frac{2}{3}$ .

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

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

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

Combine $x$ and $\frac{2}{3}$ .

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

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

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

Multiply $- \frac{2}{3} (- \frac{2}{3})$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{2}{3}$ by $1$ .

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

Multiply $\frac{2}{3}$ by $\frac{2}{3}$ .

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

Multiply $2$ by $2$ .

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

Multiply $3$ by $3$ .

$y = x^{2} - \frac{2 x}{3} - \frac{2 x}{3} + \frac{4}{9} + 2$

Subtract $\frac{2 x}{3}$ from $- \frac{2 x}{3}$ .

$y = x^{2} - 2 \frac{2 x}{3} + \frac{4}{9} + 2$

Simplify each term.

Multiply $- 2 \frac{2 x}{3}$ .

Combine $- 2$ and $\frac{2 x}{3}$ .

$y = x^{2} + \frac{- 2 (2 x)}{3} + \frac{4}{9} + 2$

Multiply $2$ by $- 2$ .

$y = x^{2} + \frac{- 4 x}{3} + \frac{4}{9} + 2$

Move the negative in front of the fraction.

$y = x^{2} - \frac{4 x}{3} + \frac{4}{9} + 2$

Step 3

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = x^{2} - \frac{4 x}{3} + \frac{4}{9} + 2 \cdot \frac{9}{9}$

Step 4

Combine $2$ and $\frac{9}{9}$ .

$y = x^{2} - \frac{4 x}{3} + \frac{4}{9} + \frac{2 \cdot 9}{9}$

Step 5

Combine the numerators over the common denominator.

$y = x^{2} - \frac{4 x}{3} + \frac{4 + 2 \cdot 9}{9}$

Step 6

Simplify the numerator.

Multiply $2$ by $9$ .

$y = x^{2} - \frac{4 x}{3} + \frac{4 + 18}{9}$

Add $4$ and $18$ .

$y = x^{2} - \frac{4 x}{3} + \frac{22}{9}$

Step 7

Reorder terms.

$y = x^{2} - (\frac{4}{3} x) + \frac{22}{9}$

Step 8

Remove parentheses.

$y = x^{2} - \frac{4}{3} x + \frac{22}{9}$

Step 9

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

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