Question

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?

Answer 1

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 `(0,0): forall a in RR: a!=0`

Explanation:

`y = aabsx`

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, -1/2, 1/2`

Graph 1 `(a=-2)` `y<0: forall x in RR`
Slope: `+2` for `x in (-oo,0)` and `-2` for `x in (0, oo)`
graph{-2absx [-10, 10, -5, 5]}

Graph 2 `(a=-1/2)` `y<0: forall x in RR`
Slope: `+1/2` for `x in (-oo,0)` and `-1/2` for `x in (0, oo)`
graph{-1/2absx [-10, 10, -5, 5]}

Graph 3 `(a=1/2)` `y>0: forall x in RR`
Slope: `-1/2` for `x in (-oo,0)` and `+1/2` for `x in (0, oo)`
graph{1/2absx [-10, 10, -5, 5]}

The vertex of `y` is `(0,0): forall a in RR: a!=0`