Answer
$(-.36538, 5.79)$
Work Step by Step
$f(x)=-5.2x^2-3.8x+5.1$
Vertex is at $x=-b/2a$
$x=-(-3.8)/2*-5.2$
$x=3.8/-10.4$
$x=-.36538$
$f(x)=-5.2x^2-3.8x+5.1$
$f(-.36538)=-5.2*(-.36538)^2-3.8*(-.36538)+5.1$
$f(-.36538)=-5.2*(.1335)+1.388444+5.1$ $f(-.36538)=-.6942+6.488444$
$f(-.36538)=5.794244$
$f(-.36538)=5.79$