Question

What is the vertex form of `y = 12x^2 - 6x + 8`?

Answer 1

`y = 12(x + frac(1)(4))^2 + frac(29)(4)`

Explanation:

You can get this equation into vertex form by completing the square

First, factor out the coefficient of the largest power of x:
`y = 12(x^2 - frac(1)(2)x) + 8`

then take half of the coefficient of the x to the first power and square it
`frac(1)(2) * frac(1)(2) = frac(1)(4) rightarrow frac(1)(4)^2 = frac(1)(16)`

add and subtract the number you just found within the parenthesis
`y = 12(x^2 + frac(1)(2)x + frac(1)(16) - frac(1)(16)) + 8`

take the negative `frac(1)(16)` out of the parenthesis
`y = 12(x^2 + frac(1)(2)x + frac(1)(16)) - frac(3)(4) + 8`

factor and simplify
`y = 12(x + frac(1)(4))^2 + frac(29)(4)` `leftarrow` answer