# How do you find the coordinates of the vertex y= -6x^2 + 14x?

Aug 13, 2016

$P = \left(\frac{7}{6} , 10.5\right)$

#### Explanation:

$y = - 6 {x}^{2} + 14 x$

$\text{Let the coordinates of vertex be } P \left(x , y\right)$

$\text{Take derivative of the function }$

$\frac{d y}{d x} = - 12 x + 14$

$\text{Now calculate } \frac{d y}{d x} = 0$

$- 12 x + 14 = 0$

$12 x = 14$

$x = \frac{14}{12} = \frac{7}{6} \text{ (This is the x coordinate of vertex)}$

$\text{calculate "f(x) " to find the y coordinate of vertex}$

$\text{plug x=" 7/6 " into y}$

$y = - 6 \cdot {\left(\frac{7}{6}\right)}^{2} + 14 \cdot \frac{7}{6}$

$y = - \frac{49}{6} + \frac{98}{6}$

$y = \frac{49}{6}$

$y = \left(\text{This is the y coordinate of vertex}\right)$

$\text{Thus}$

$P = \left(\frac{7}{6} , 8.17\right)$