y=-x^2-4x-2 complete the square and graph-how do I know the points on the graph?

Question

y=-X^2-4x-2; Complete the square-and then graph.  How do I graph?  I get y=(x+2)^2-2  but not sure how to graph.

 

Do I divide the -1 coefficient?

Answer 1

y=-x^2-4x-2 can be written as -(x^2+4x+2)=-(x^2+4x+4-4+2)=-(x+2)^2+2. That completes the square. When y=0,

-(x+2)^2+2=0, so (x+2)^2=2, and x+2=+/-sqrt(2). So x=-2+/-sqrt(2). These are the roots.

The graph resembles an inverted U with widening arms. It cuts the y axis when x=0 at y=-2, and it cuts the x axis as above, both values of x being negative (approx -0.6 and -3.4), so the upturned U's right arm cuts the y axis at -2 and the "hump" of the U lies to the left of the y axis. The highest point of the U (vertex) lies halfway between the roots at (-2,2) (when x=-2, y=-4+8-2=2). I hope this helps you to draw the graph.