# How do you graph the quadratic function and identify the vertex and axis of symmetry and x intercepts for y=-(x+3)(x+5)?

Dec 28, 2017

x-intercepts: $x = - 5 \mathmr{and} x = - 3$
Axis of Symmetry: $x = - 4$
Vertex: $\left(- 4 , 1\right)$

#### Explanation:

x-intercepts:
Use the Null Factor Law
$x + 3 = 0$
$x = - 3$
and
$x + 5 = 0$
$x = - 5$

Axis of Symmetry:
Halfway between the two x-intercepts.
$x = \frac{- 3 + \left(- 5\right)}{2} = - 4$

Vertex:
The function evaluated at the axis of symmetry
$f \left(- 4\right) = - \left(- 4 + 3\right) \left(- 4 + 5\right) = 1$
Vertex: $\left(- 4 , 1\right)$