# What is the vertex form of y=1/5x^2+7/13x-2?

Sep 17, 2017

$y = \left(\frac{1}{5}\right) {\left(x + \frac{35}{36}\right)}^{2} - \frac{1597}{676}$

#### Explanation:

$y = \frac{{x}^{2}}{5} + \frac{7 x}{13} - 2$
x-coordinate of vertex:
$x = - \frac{b}{2 a} = \left(\frac{- 7}{13}\right) \left(\frac{5}{2}\right) = - \frac{35}{26}$
y-coordinate of vertex:
y(-35/26) = (1/5)(1225)/676) - (7/13)(35/26) - 2 =
= 245/676 - 245/338 - 2 = - 245/676 - 1352/676 =
= - 1597/676
Factored form of y:
$y = a {\left(x + \frac{b}{2 a}\right)}^{2} + y \left(- \frac{b}{2 a}\right)$
$y = \left(\frac{1}{5}\right) {\left(x + \frac{35}{26}\right)}^{2} - \frac{1597}{676}$