Find the symmetry and vertex of the function F(x)= negative four x raised to the second power plus sixteen x minus eight

F(x)  =  -4x² + 16 x - 8

The x-value of the vertex can be found by using the formula:  -b/(2a).

For this problem,  a = -4,  b = 16, and  c = -8.

x-value  =  -b/(2a)  =  -16/(2·-4)  =  -16/-8  =  2

If  x = 2, F(2)  =  -4(2)² + 16(2) - 8  =  8

So, the vertex is  (2, 8).

The equation of the line of symmetry is the equation of the vertical line that passes through the vertex. This equation is:  x  =  2.