Question

What is the vertex of `y= -6x^2 + 4x + 3`?

Answer 1

Vertex: `(1/3, 3 2/3)`

Explanation:

Probably the easiest way to do this is to convert the equation into "vertex form": `y=m(x-a)^2+b` with vertex at `(a,b)`

Given:
`color(white)("XXX")y=-6x^2+4x+3`

Extract the `m` factor
`color(white)("XXX")y= (-6)(x^2-2/3x)+3`

Complete the square
`color(white)("XXX")y=(-6)(x^2-2/3x+(1/3)^2)+3-(-6)*(1/3)^2`

Rewrite with a squared binomial and simplified constant
`color(white)("XXX")y=(-6)(x-1/3)^2+ 3 2/3`

which is in vertex form with vertex at `(1/3, 3 2/3)`