# What is the vertex form of 5y=3x^2 -2x +8?

Aug 9, 2017

$\left(\frac{1}{3} , \frac{23}{15}\right)$

#### Explanation:

$5 y = 3 {x}^{2} - 2 x + 8$
$5 y = 3 \left[{x}^{2} - \left(\frac{2}{3}\right) x\right] + 8$
$5 y = 3 \left[{x}^{2} - \left(\frac{2}{3}\right) x + {\left(\frac{1}{3}\right)}^{2}\right] + 8 - \frac{1}{3}$
$5 y = 3 {\left(x - \frac{1}{3}\right)}^{2} + \frac{23}{3}$
$y = \frac{3}{5} {\left(x - \frac{1}{3}\right)}^{2} + \frac{23}{15}$ => in the vertex form of:
$y = a {\left(x - h\right)}^{2} + k$ => where $\left(h , k\right)$ is the vertex, thus the vertex is:
$\left(\frac{1}{3} , \frac{23}{15}\right)$