Question

What is the vertex form of `y=9x^2-12x+4`?

Answer 1

The given equation can be written as
`=>y=(3x)^2-2*3x*2+2^2`
`=>y=(3x-2)^2`
`=>y=(3(x-2/3))^2`
`=>y=9(x-2/3)^2`
Now putting, `y =Y` and `x-2/3=X` b we have

`=>Y=9X^2`
this equation has vertex `(0,0)`
So puttinf `X=0`and `Y =0` we get

`x=2/3 and y=0`

So coordinate of vertex is `(2/3,0)` as evident fom the graph below

graph{9x^2-12x+4 [-3.08, 3.08, -1.538, 1.541]}