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?

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Answer 1 · 2017-10-14T03:06:07

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

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

$y = aabsx$

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