Write in Standard Form y=2(x+5/4)^2-49/8

$y = 2 {(x + \frac{5}{4})}^{2} - \frac{49}{8}$

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 ${(x + \frac{5}{4})}^{2}$ as $(x + \frac{5}{4}) (x + \frac{5}{4})$ .

$y = 2 ((x + \frac{5}{4}) (x + \frac{5}{4})) - \frac{49}{8}$

Expand $(x + \frac{5}{4}) (x + \frac{5}{4})$ using the FOIL Method.

Apply the distributive property.

$y = 2 (x (x + \frac{5}{4}) + \frac{5}{4} \cdot (x + \frac{5}{4})) - \frac{49}{8}$

Apply the distributive property.

$y = 2 (x \cdot x + x (\frac{5}{4}) + \frac{5}{4} \cdot (x + \frac{5}{4})) - \frac{49}{8}$

Apply the distributive property.

$y = 2 (x \cdot x + x (\frac{5}{4}) + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$y = 2 (x^{2} + x (\frac{5}{4}) + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Combine $x$ and $\frac{5}{4}$ .

$y = 2 (x^{2} + \frac{x \cdot 5}{4} + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

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

$y = 2 (x^{2} + \frac{5 \cdot x}{4} + \frac{5}{4} x + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Combine $\frac{5}{4}$ and $x$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{5}{4} \cdot \frac{5}{4}) - \frac{49}{8}$

Multiply $\frac{5}{4} \cdot \frac{5}{4}$ .

Multiply $\frac{5}{4}$ by $\frac{5}{4}$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{5 \cdot 5}{4 \cdot 4}) - \frac{49}{8}$

Multiply $5$ by $5$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{25}{4 \cdot 4}) - \frac{49}{8}$

Multiply $4$ by $4$ .

$y = 2 (x^{2} + \frac{5 x}{4} + \frac{5 x}{4} + \frac{25}{16}) - \frac{49}{8}$

Add $\frac{5 x}{4}$ and $\frac{5 x}{4}$ .

$y = 2 (x^{2} + 2 (\frac{5 x}{4}) + \frac{25}{16}) - \frac{49}{8}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = 2 (x^{2} + 2 (\frac{5 x}{2 (2)}) + \frac{25}{16}) - \frac{49}{8}$

Cancel the common factor.

$y = 2 (x^{2} + 2 (\frac{5 x}{2 \cdot 2}) + \frac{25}{16}) - \frac{49}{8}$

Rewrite the expression.

$y = 2 (x^{2} + \frac{5 x}{2} + \frac{25}{16}) - \frac{49}{8}$

Apply the distributive property.

$y = 2 x^{2} + 2 (\frac{5 x}{2}) + 2 (\frac{25}{16}) - \frac{49}{8}$

Simplify.

Cancel the common factor of $2$ .

Cancel the common factor.

$y = 2 x^{2} + 2 (\frac{5 x}{2}) + 2 (\frac{25}{16}) - \frac{49}{8}$

Rewrite the expression.

$y = 2 x^{2} + 5 x + 2 (\frac{25}{16}) - \frac{49}{8}$

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$y = 2 x^{2} + 5 x + 2 (\frac{25}{2 (8)}) - \frac{49}{8}$

Cancel the common factor.

$y = 2 x^{2} + 5 x + 2 (\frac{25}{2 \cdot 8}) - \frac{49}{8}$

Rewrite the expression.

$y = 2 x^{2} + 5 x + \frac{25}{8} - \frac{49}{8}$

Step 3

Combine fractions.

Combine the numerators over the common denominator.

$y = 2 x^{2} + 5 x + \frac{25 - 49}{8}$

Simplify the expression.

Subtract $49$ from $25$ .

$y = 2 x^{2} + 5 x + \frac{- 24}{8}$

Divide $- 24$ by $8$ .

$y = 2 x^{2} + 5 x - 3$

Step 4

Write in Standard Form y=2(x+5/4)^2-49/8

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