Answer
$x=0.6m$ and $x=4.6m$
Work Step by Step
We can find the required locations as follows:
$E=\frac{1}{2}mv^2+U$
We plug in the known values to obtain:
$E=\frac{1}{2}(1.34)(1.25)+6.0$
$E=7.0J$
When we draw a horizontal line on the plot at $U=7.0 J$, we obtain the approximate locations as $x=0.6m$ and $x=4.6m$ and these are the turning points of the object.