# What is the vertex form of  f(x) = -3x^2 + 3x-2 ?

Dec 10, 2017

$f \left(x\right) = - 3 {\left(x - \frac{1}{2}\right)}^{2} - \frac{5}{4}$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

$\text{given the parabola in "color(blue)"standard form}$

f(x)=ax^2+bx+c color(white)(x);a!=0

$\text{then the x-coordinate of the vertex is}$

•color(white)(x)x_(color(red)"vertex")=-b/(2a)

$f \left(x\right) = - 3 {x}^{2} + 3 x - 2 \text{ is in standard form}$

$\text{with "a=-3,b=3" and } c = - 2$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{3}{- 6} = \frac{1}{2}$

$\text{substitute this value into the equation for y}$

${y}_{\textcolor{red}{\text{vertex}}} = - 3 {\left(\frac{1}{2}\right)}^{2} + 3 \left(\frac{1}{2}\right) - 2 = - \frac{5}{4}$

$\Rightarrow f \left(x\right) = - 3 {\left(x - \frac{1}{2}\right)}^{2} - \frac{5}{4} \leftarrow \textcolor{red}{\text{in vertex form}}$