Complete the square as an aid in graphing

Question

Answer 1

y=-x^2 -4x -6

= -(x^2 +4x +4) -6 +4

= -(x+2)^2 -2 is a downward opening parabola with vertex = maximum point = (-2,-2)

it's in the vertex form

y =a(x-h)^2 + k where (h,k) is the vertex. if a<0, it's a downward opening vertical parabola

y intercept = (0,-6)

x intercept DNE, it never crosses the y axis

axis of symmetry is x=-2

so (-4,-6) is also a point on the parabola, as it's an equal distance of 2 from x=-2, as is (0,6)

plot those 3 points, connect them with a smooth parabolic curve