y = -5x^2+17x-12

We can find the line of symmetry by finding the x coordinate of the vertex....this is given by

-17 / (2 * -5) = -17/-10 = 17/10

So...the equation for the line of symmetry is just x = 17/10

Here's a graph : https://www.desmos.com/calculator/gckwjghnxa