Question 260499
The equation is for a parabola. The standard form of a parabola is:

y = ax^2 + bx + c 
The role of 'a' 
If a> 0, the parabola opens upwards 
if a< 0, it opens downwards. 
The axis of symmetry 
The axis of symmetry is the line x = -b/2a 

For this parabola we have a = -3, b = -6 and c = -5.

So the parabola opens downward and is symmetric around the vertical line
x = -b/2a = -(-6)/(2*(-3)) = 6/-6 = -1.

The maximum value for y will occur when x = -1. 
When x = -1, y = -3*(-1)^2 -6*(-1) - 5 = -3 + 6 - 5 = -2

To get the shape of the parabola choose values of x on either side of -1, say x = 0 and x = -2 and compute the corresponding values for y. 

Use the quadratic formula to solve: 

-3x^2 - 6x - 5 = 0.

It will turn out there are no real solutions.