# In the same coordinate plane, graph y= a l xl for a = -2,-1/2, 1/2. What effect does A have on the graph of y= alxl? what is the vertex of the graph of y= a lxl?

Oct 14, 2017

The coefficient $a$ determines the sign of $y$ and slope of $y$ for both negative and positive values of $x$

The vertex of $y$ is $\left(0 , 0\right) : \forall a \in \mathbb{R} : a \ne 0$

#### Explanation:

$y = a \left\mid x \right\mid$

The coefficient $a$ determines the sign of $y$ and slope of $y$ for both negative and positive values of $x$.

Consider the three graphs of $y$ below where $a = - 2 , - \frac{1}{2} , \frac{1}{2}$

Graph 1 $\left(a = - 2\right)$ $y < 0 : \forall x \in \mathbb{R}$
Slope: $+ 2$ for $x \in \left(- \infty , 0\right)$ and $- 2$ for $x \in \left(0 , \infty\right)$
graph{-2absx [-10, 10, -5, 5]}

Graph 2 $\left(a = - \frac{1}{2}\right)$ $y < 0 : \forall x \in \mathbb{R}$
Slope: $+ \frac{1}{2}$ for $x \in \left(- \infty , 0\right)$ and $- \frac{1}{2}$ for $x \in \left(0 , \infty\right)$
graph{-1/2absx [-10, 10, -5, 5]}

Graph 3 $\left(a = \frac{1}{2}\right)$ $y > 0 : \forall x \in \mathbb{R}$
Slope: $- \frac{1}{2}$ for $x \in \left(- \infty , 0\right)$ and $+ \frac{1}{2}$ for $x \in \left(0 , \infty\right)$
graph{1/2absx [-10, 10, -5, 5]}

The vertex of $y$ is $\left(0 , 0\right) : \forall a \in \mathbb{R} : a \ne 0$