# How do you find the vertex of y= -2(x+3)(x-1)?

May 15, 2018

$\text{vertex } = \left(- 1 , 8\right)$

#### Explanation:

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

$\text{to find the zeros set } y = 0$

$\Rightarrow - 2 \left(x + 3\right) \left(x - 1\right) = 0$

$\text{equate each factor to zero and solve for } x$

$x + 3 = 0 \Rightarrow x = - 3$

$x - 1 = 0 \Rightarrow x = 1$

${x}_{\text{vertex}} = \frac{- 3 + 1}{2} = - 1$

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

${y}_{\text{vertex}} = - 2 \left(2\right) \left(- 2\right) = 8$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 1 , 8\right)$