# What is the vertex form of y= -9x^2+11x-1?

Apr 27, 2017

$y = - 9 {\left(x - \frac{11}{18}\right)}^{2} + \frac{85}{36}$

#### Explanation:

The equation of a parabola in $\textcolor{b l u e}{\text{vertex form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where (h ,k) are the coordinates of the vertex and a is a constant.

$\text{using the method of "color(blue)"completing the square}$

add (1/2"coefficient of x-term")^2" to " x^2-11/9x

Since we are adding a value that is not there we must also subtract it.

$\text{that is add/subtract} {\left(\frac{- \frac{11}{9}}{2}\right)}^{2} = \frac{121}{324}$

$\text{the coefficient of " x^2" term must be 1}$

$y = - 9 \left({x}^{2} - \frac{11}{9} x\right) - 1 \leftarrow \textcolor{red}{\text{ coefficient now 1}}$

$\Rightarrow y = - 9 \left({x}^{2} - \frac{11}{9} x \textcolor{red}{+ \frac{121}{324} - \frac{121}{324}}\right) - 1$

$\textcolor{w h i t e}{\Rightarrow y} = - 9 {\left(x - \frac{11}{18}\right)}^{2} + \frac{121}{36} - 1$

$\textcolor{w h i t e}{\Rightarrow y} = - 9 {\left(x - \frac{11}{18}\right)}^{2} + \frac{85}{36} \leftarrow \textcolor{red}{\text{ in vertex form}}$