Question

How do you find the axis of symmetry, and the maximum or minimum value of the function `y=4(x+3)^2-4`?

Answer 1

`"vertex " : (-3, -4)`
`"minimum value " : -4`

Explanation:

`y = a(x - h)^2 + k` is the Vertex Form of parabola,
`"Vertex " : (h, k)`

`y=4(x+3)^2-4`
`"Vertex " : (-3, -4)`

The axis of symmetry intersects a parabola at its vertex.
`"axis of symmetry" : x = -3`

`a = 4 > 0 =>` The parabola opens upward and has a minimum value at vertex:
The minimum value of y is -4.

https://www.desmos.com/calculator/zaw7kuctd3