Answer:
1. y = x^2 + 6x + 2 = x^2 + 6x + 9 - 7 = (x + 3)^2 - 7
The vertex of the parabola whose equation is y = x^2 + 6x + 2 is (-3, -7).
2. y = 3x^2 + 24x - 1 = 3(x^2 + 8x) - 1 = 3(x^2 + 8x + 16) - 1 - 48 = 3(x + 4)^2 - 49
The line of symmetry for the parabola whose equation is y = 3x^2 + 24x - 1 is x = -4
3. y = x^2 + 10x + 25 = (x + 5)^2
The line of symmetry for the parabola whose equation is y = x^2 + 10x + 25 is x = -5
4. y = -2x^2 + 8x - 5 = -2(x^2 - 4x) - 5 = -2(x^2 - 4x + 4) - 5 + 8 = -2(x - 2)^2 + 3
The vertex of the parabola whose equation is y = -2x^2 + 8x - 5 is (2, 3).
5. y = x^2 - 12x + 7 = x^2 - 12x + 36 - 29 = (x - 6)^2 - 29
The line of symmetry for the parabola whose equation is y = x^2 - 12x + 7 is x = 6
6. y = x^2 - 4x + 6 = x^2 - 4x + 4 + 2 = (x - 2)^2 + 2
The vertex of the parabola whose equation is y = x^2 - 4x + 6 is (2, 2).