In order to do this you have to put it into vertex form, which is achieved by completing the square. Start out by setting it equal to 0. [tex]-2 x^{2} +8x-5=0[/tex]. Next, move the 5 over to the other side of the equals sign. [tex]-2 x^{2} +8x=5[/tex]. In order to complete the square, the rule is that the leading coefficient on the squared term is a positive 1. Ours is a -2, so we have to factor it out. [tex]-2( x^{2} -4x)=5[/tex]. Complete the square by taking half the linear term (the linear term is 4 now), square it and add it to both sides. Half of 4 is 2, and 2 squared is 4, so we will add it in. HOWEVER, when you add it into the parenthesis on the left, you still have that -2 hanging out front, so what you really have added in is -2(4) which is -8. Here's what we have now so far: [tex]-2( x^{2} -4x+4)=5-8[/tex] which simplifies to [tex]-2( x^{2} -4x+4)=-3[/tex]. The next step is to create the perfect square binomial we formed during this process on the left, which gives us [tex]-2(x-2) ^{2}=-3[/tex]. Move the -3 back over to the other side by addition and you get [tex]-2(x-2) ^{2} +3=y[/tex]. This tells us that our vertex is (2, 3)
