Write in Standard Form y=1/2(x-2)^2-4

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

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 $(x - 2) (x - 2)$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 2$ by $- 2$ .

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

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

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

Apply the distributive property.

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

Simplify.

Combine $\frac{1}{2}$ and $x^{2}$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Subtract $4$ from $2$ .

$y = \frac{x^{2}}{2} - 2 x - 2$

Step 4

Reorder terms.

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

Step 5

Write in Standard Form y=1/2(x-2)^2-4

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