# How do you write y = - 3x^2 + 5x - 2 in vertex form?

Jun 2, 2016

$y = - 3 {\left(x - \frac{5}{6}\right)}^{2} + \frac{1}{12}$

#### Explanation:

Equation in standard form

$y = - 3 {x}^{2} + 5 x - 2$

Vertex form of the equation is -

$y = a {\left(x - h\right)}^{2} + k$

Where -

$a$ is coefficient of ${x}^{2}$
$h$ is the x-coordinate of the vertex
$k$ is y-coordinate of the vertex

$h = \frac{- b}{2 a} = \frac{- 5}{2 \times - 3} = \frac{- 5}{- 6} = \frac{5}{6}$

$k = - 3 {\left(\frac{5}{6}\right)}^{2} + 5 \left(\frac{5}{6}\right) - 2$

$k = - 3 \left(\frac{25}{36}\right) + \frac{25}{6} - 2 = - \frac{25}{12} + \frac{25}{6} - 2 = \frac{1}{12}$

The equation is -

$y = - 3 {\left(x - \frac{5}{6}\right)}^{2} + \frac{1}{12}$