Question

How do you find the vertex of `y = 3x^2 -6x-4`?

Answer 1

Convert to vertex form to obtain the vertex at `(1,-7)`

Explanation:

The easiest way to solve this requirement is to rewrite the equation into vertex form:
`color(white)("XXXX")` `y = m(x-a)^2+b`
`color(white)("XXXX")` `color(white)("XXXX")`which will have a vertex at `(a,b)`

Given `y = 3x^2-6x-4`

Extract `m`
`color(white)("XXXX")` `y = 3(x^2-2x) -4`

Complete the square by adding `3(1)` and then subtracting `3` as
`color(white)("XXXX")` `y = 3(x^2-2x+1) -4 -3`

Rewrite as a squared binomial and simply
`color(white)("XXXX")` `y = 3(x-1)^2 + (-7)`

Since this is in vertex form, we can simply read the vertex off as:
`color(white)("XXXX")` `(1,-7)`