+118613 graphing
\(y=-3x^2-24x-52\\ \text{axis of symmetry } \\x = \frac{-b}{2a}=\frac{24}{-6}=-4\)
Since this polynomial is of order 2 (x squared that is) This is a parabola
Since the leading coefficent ( the -3 in front of the x^2) is negative, this parabola is concave down.
When x=0, y=-52 so the y intercept is -52
The axis of symmetry is x=-4
The vertex will be x=-4
\(y=-3*16-24*-4-52\\ y=-48+96-52\\ y=-48+96-52\\ y=-4\\ \text{So the maximum is (-4,-4)}\)
now we know another point is (0,-52) and using symmetry another will be (-8,-52)
These don't fit on your graph paper unfortunately so I gues you could find the y value when x=-2
\(y=-3x^2-24x-52\\ y=-3*4-24*-2-52\\ y=-12+48-52\\ y=-16\\\)
So 2 more points are (-2,-16) and (-6,-16)
Now you can plot them
Here is the graph using Desmos Graphing calculator
