Question

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

Answer 1

To graph this you can just construct a table of values and plot the values. Or you could base it off the vertex, and solutions (if any)

Based on the equation you've given, `y=2(x+2)^2-4`, the vertex is `(-2, -4)`, because vertex form is `y=a(x – h)2+k` where `h` is the x-coordinate and `k` is the y-coordinate of the vertex.

The x-coordinate of the vertex is also the axis of symmetry, which is `x=-2`.

As mentioned above, if you have the vertex and solutions, you can plot the graph with substantial accuracy, but if you have no solutions, then it is best to construct a table of values for a range of `x` values and go from there.