Question 130757
To find the x-coordinate of the vertex, we can use this formula:


{{{x=-b/(2a)}}}


From the equation {{{f(x)=-2x^2+2x+8}}} we can see that a=-2 and b=2


{{{x=(-2)/(2*-2)}}} Plug in b=2 and a=-2



{{{x=(-2)/-4}}} Multiply 2 and -2 to get -4




{{{x=1/2}}} Reduce



So the x-coordinate of the vertex is  {{{x=1/2}}}



In turn, this means that the equation of the line of symmetry is also {{{x=1/2}}} (since the line goes through the vertex)