# What is the axis of symmetry and vertex for the graph y= -7x^2 +2x?

Jul 7, 2018

$x = \frac{1}{7} , \text{ vertex } = \left(\frac{1}{7} , \frac{1}{7}\right)$

#### Explanation:

$\text{calculate the zeros by letting y = 0}$

$- 7 {x}^{2} + 2 x = 0$

$x \left(- 7 x + 2\right) = 0$

$x = 0 , x = \frac{2}{7} \leftarrow \textcolor{b l u e}{\text{are the zeros}}$

$\text{the vertex lies on the axis of symmetry which is}$
$\text{situated at the midpoint of the zeros}$

$\text{axis of symmetry } x = \frac{0 + \frac{2}{7}}{2} = \frac{1}{7}$

$\text{substitute this value into the equation for y-coordinate}$

$y = - 7 {\left(\frac{1}{7}\right)}^{2} + 2 \left(\frac{1}{7}\right) = - \frac{1}{7} + \frac{2}{7} = \frac{1}{7}$

$\textcolor{m a \ge n t a}{\text{vertex }} = \left(\frac{1}{7} , \frac{1}{7}\right)$
graph{-7x^2+2x [-10, 10, -5, 5]}