Converting from vertex form to standard form y = (1)/(2) (x - 2) {}^(2) - 4 ​

Question

Converting from vertex form to standard form


`y = (1)/(2) (x - 2) {}^(2) - 4`
​

Answer 1

`\displaystyle f(x)=(1)/(2)x^2-2x-2`

Explanation:

To convert from vertex form to standard form, we can simply expand.

So, we have:

`\displaystyle f(x)=(1)/(2)(x-2)^2-4`

Expand the square:

`\displaystyle f(x)=(1)/(2)(x^2-4x+4)-4`

Distribute:

`\displaystyle f(x)=(1)/(2)x^2-2x+2-4`

Simplify:

`\displaystyle f(x)=(1)/(2)x^2-2x-2`