Frozen: It's Coronation Day!

Algebra Level 2

When Anna realises that it is Coronation day she starts singing and fantasising about meeting "the one". Then she starts dancing with a head and accidentally lets go and throws the head across the room onto a cake.

If Anna is at point $(5,0)$ on the cartesian co-ordinate plane and the cake is at $(-3,0)$ , the flight path of the head can be described by the equation:

$y=-2x^2+bx+c$

Find the value of $b+c$