# How do you write f(x) = -3x^2 + 3x - 2 in vertex form?

Jul 26, 2016

f(x) = -3(x - 1/2)^2 - 5/4

#### Explanation:

First find the coordinate of the vertex>
x-coordinate of vertex:
$x = - \frac{b}{2 a} = - \frac{3}{-} 6 = \frac{1}{2}$
y-coordinate of vertex:
$y \left(\frac{1}{2}\right) = - 3 \left(\frac{1}{4}\right) + 3 \left(\frac{1}{2}\right) - 2 = - \frac{3}{4} + \frac{3}{2} - 2 = - \frac{5}{4}$
Vertex form of y:
$f \left(x\right) = - 3 {\left(x - \frac{1}{2}\right)}^{2} - \frac{5}{4}$