The equation of the parabola is expressed as
y = - x^2 - 6x - 10
We would substitute values for x into the equation and find the corresponding values for y. Thus,
if x = - 1, y = - (- 1)^2 - 6(-1) - 10 = - 1 + 6 - 10 = - 5
if x = 0, y = - (0)^2 - 6(0) - 10 = - 10
if x = 1, y = - (1)^2 - 6(1) - 10 = - 1 - 6 - 10 = - 17
if x = 2, y = - (2)^2 - 6(2) - 10 = - 4 - 12 - 10 = - 26
We would plot the values of x and y on the horizontal and vertical axes of the graph respectively. The graph is shown below
Looking at the top of the parabola,
x = - 3 and y = - 1
Thus, the vertex is (- 3, - 1)