Question

What is the vertex form of `y=-9x^2 +12x - 18`?

Answer 1

Below is the proof (a completion of square)

Explanation:

`y = -9x^2 + 12x - 18`

`y = -9(x^2 - 12/9x) - 18`

`y = -9(x^2 - 12/9x +`_ - _ ) - 18#

`_ = ((-12/9) / 2)^2`

`_ = 4/9`

`y = -9(x^2 - 12/9x + 4/9) - 4/9(-9) - 18`

`y= -9(x - 2/3)^2 - 14`

So, `y = -9x^2 + 12x - 18` is equal to `y = -9(x - 2/3)^2 - 14`

Hopefully that explanation helped!