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

Mar 12, 2016

The given equation can be written as
$\implies y = {\left(3 x\right)}^{2} - 2 \cdot 3 x \cdot 2 + {2}^{2}$
$\implies y = {\left(3 x - 2\right)}^{2}$
$\implies y = {\left(3 \left(x - \frac{2}{3}\right)\right)}^{2}$
$\implies y = 9 {\left(x - \frac{2}{3}\right)}^{2}$
Now putting, $y = Y$ and $x - \frac{2}{3} = X$ b we have

$\implies Y = 9 {X}^{2}$
this equation has vertex $\left(0 , 0\right)$
So puttinf $X = 0$and $Y = 0$ we get

$x = \frac{2}{3} \mathmr{and} y = 0$

So coordinate of vertex is $\left(\frac{2}{3} , 0\right)$ as evident fom the graph below

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