Answer
See graph (red).
vertex $(3,5)$, axis of symmetry $x=3$.
Work Step by Step
1. Given $f(x)=-2x^2+12x-13=-2(x^2-6x+9)+5=-2(x-3)^2+5$, we can obtain its graph from $y=x^2$ by shifting the curve 3 units to the right, stretching vertically by a factor of 2, reflecting across the x-axis, then shifting 5 units up. See graph (red).
2. We can find its vertex $(3,5)$, axis of symmetry $x=3$.
