Answer
vertex $(3,5)$, axis of symmetry $x=3$.
See graph.
Work Step by Step
Step 1. Rewrite the function as $f(x)=-2(x^2-6x+9)+18-13=-2(x-3)^2+5$, we can find its vertex $(3,5)$ and axis of symmetry $x=3$
Step 2. To obtain the graph of $f$ from $y=x^2$, shift the curve 3 units to the right, stretch vertically by a factor of 2, reflect across the x-axis, then shift 5 units up. See graph.
