How do you tell whether the graph opens up or down, find the vertex, and find the axis of symmetry given y=-x^2-1?

1 Answer
Jun 16, 2018

Graph opens down.
Vertex at (0,-1);Axis of Symmetry: x=0

Explanation:

y = -x^2-1

y is a quadratic function of the from: ax^2+bx+c
Where: a=-1, b=0 and c=-1

Since y is a quadratic its graph will be a parabola.

Since a<0 y will have a maximum value at its vertex.

Now, since y is a parabola with a maximum value it must open downwards.

The vertex of y will lie on its axis of symmetry where x = (-b)/(2a) i.e. where x=0

Since, y(0) = -1 -> y_"vertex" = (0,-1)

The axis of symmetry of y is the vertical line x=0 which is the y-axis.

We can see these results from the graph of y below.
graph{ -x^2-1 [-13.28, 12.03, -7.17, 5.49]}