Find the vertex of each parabola

y=x^2-4x+2

y=4-6x-3x^2

y=2x^+8x-13

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).