Question

What is the vertex form of `y=4x^2-13x-6`?

Answer 1

`y = 4(x-13/8)^2-265/16`

Explanation:

`y = 4x^2-13x-6`

`= 4(x^2-13/4xcolor(white)"XXXXXX") -6`

`1/2 * 13/4 = 13/8` and `(13/8)^2 = 169/64`

So inside the parentheses add `169/64`

Outside the parentheses subtract `4 * 169/64 = 169/16`

`y = 4(x^2-13/4+169/64) - 169/16 - 96/16`

To finish, factor the expression in parentheses and simplify the subtraction outside the parentheses.

`y = 4(x-13/8)^2-265/16`