Question

Write y = 2x2-12x+25 in vertex form, plz show work.

Answer 1

The vertex form of the equation is
`y=2(x-3)^2+7`

Explanation:

Given equation in standard form:

`y=2x^2-12x+25`

Completing square method:

Equating the given function to
`0`.

`2x^2-12x+25=0`

Subtracting both sides by
`25`.

`2x^2-12x+25-25=0-25`

`2x^2-12x=-25`

Taking common factor
`2x`.

`2(x^2-6x)=-25`

Dividing
`-6` by
`2` then adding and subtracting the square of it from the whole term in parenthesis

`2(x-6x+((6)/(2))^2-((6)/(2))^2)=-25`

`2(x^2-6x+9-9)=0`

`[x^2-6x+9]` can be written as
`(x-3)^2`.

`2((x-3)^2-9)=-25`

Using distribution.

`2(x-3)^2-18=-25`

Adding both sides by 25.

`2(x-3)^2-18+25=-25+25`

`2(x-3)^2+7=0`

Equating the above function with
`y`

`y=2(x-3)^2+7`

∴ The vertex form of the equation is
`y=2(x-3)^2+7`