# What is the the vertex of y = 7x^2 - 9x ?

Nov 29, 2015

The vertex is the point $\left(\frac{9}{14} , - \frac{81}{28}\right)$

#### Explanation:

The vertex of such a parabola is the minimum of the parabola. So, we can derive the equation to obtain

$14 x - 9$

To seek a maximum, set the derivative to zero:

$14 x - 9 = 0 \setminus \iff 14 x = 9 \setminus \iff x = \frac{9}{14}$

So, the $y$ coordinate of the maximum is

$7 {\left(\frac{9}{14}\right)}^{2} - 9 \left(\frac{9}{14}\right) = - \frac{81}{28}$