How do you graph and label the vertex and axis of symmetry of #y=-2(x+1)^2-4#?

1 Answer
Jun 22, 2018

Vertex: #V(-1,-4)#
Axis of symmetry: #x=-1#

Explanation:

graph{y=-2(x+1)^2-4 [-10, 10, -5, 5]}
In #y=ax^2#, the vertex is #V(0,0)#.
If you shift the graph #b# to the left and #c# up, you get #y=a(x-b)^2+c#. The vertex is shifts along with the rest of the graph, so it becomes #V(b,c)#. In this case #b=-1# and #c=-4#, so #V(-1,-4)#.

The axis of symmetry is the vertical line that goes trough the vertex, so #x=b#. Or in this case: #x=-1#.