What are the vertex, axis of symmetry, maximum or minimum value, and range of y = 3x^2 + 6x - 1?

The vertex is when x=-b/2a, which is also the line of symmetry.

in this case, b=6, a=3, so x=-6/6=-1

when x=-1. y=3-6-1=-4

another way to do it is to write the equation into vertex form by making a square:

3x²+6x-1

3 (x²+2x-1/3)

3 (x²+2x+1-1-1/3))

3 (x²+2x+1-4/3))

notice the bold part makes a square:

3 (x+1) ²-4

Either way,

the vertex is (-1, - 4)

the axis of symmetry is x=-1

the coefficient of x² is 3, a positive number, so this parabola opens upward. the function has a minimum value of y=-4

the range is all real number larger than - 4