Question

What is the vertex form of `3y = 3x^2-4x+11`?

Answer 1

`y=(x-2/3)^2+29/9`

Explanation:

Vertex form of a quadratic equation: `y=a(x-h)^2+k`

The parabola's vertex is the point `(h,k)`.

First, divide everything by `3`.

`y=x^2-4/3x+11/3`

Complete the square using only the first `2` terms on the right. Balance the term you've added to complete the square by also subtracting it from the same side of the equation.

`y=(x^2-4/3xcolor(blue)+color(blue)(4/9))+11/3color(blue)-color(blue)(4/9`

`y=(x-2/3)^2+33/9-4/9`

`y=(x-2/3)^2+29/9`

From this, we can determine that the vertex of the parabola is at the point `(2/3,29/9)`.