Question

How do you rewrite the equation in vertex form: `4x^2+16-9`?

Answer 1

Version 1: Where I assume an `x` was accidentally missed on the `+16` term:
`y=4x^2+16x-9`

Vertex form of a quadratic is
`y = m(x-a)^2+b`
where the vertex of the parabola is at `(a,b)`

`y=4x^2+16x-9`

`=4(x^2+4x)-9 " extracting the "m" factor"`

#= 4(x^2+4x+2^2) -16 -9" completing the square"#

`=4(x+2)-25 " simplifying"`

`=4(x-(-2)) +(-25)" into vertex form"`

(The vertex is at `(x,y) =(-2,-25)`)

Version 2: Where the question was entered correctly (except for the missing `(y=)` which is needed to make it an equation
`y=4x^2+16-9`
which is equivalent to `y=4x^2+7`

This can be rearranged as
`y=4(x-0)^2+7`
for a parabola with a vertex at `(x,y)=(0,7)`