# How do you graph and find the vertex for  y=6abs(x-7)?

May 27, 2015

$y = 6 \left\mid x - 7 \right\mid$

When $x < 7$
$y = 6 \left(7 - x\right) = 42 - 6 x$ which is the equation of a straight line terminating at $\left(7 , 0\right)$

When $x \ge 7$
$y = 6 \left(x - 7\right) = 6 x - 42$ which is also the equation of a straight line terminating at $\left(7 , 0\right)$

The vertex is at $\left(7 , 0\right)$

graph{6*abs(x-7) [3.743, 9.902, -0.382, 2.696]}