Need some help on the highlighted questions below.

Question

Answer 1

7 y=2x^2 + 3 has vertex (0,3) and axis of symmetry x=0 or the y axis

general standard upward opening parabola is y=a(x-h)^2 + k where (h,k) is the vertex and x=h is the axis of symmetry

8 y=-3x^2 + 12x + 1

y=-3(x^2 -4x) +1

complete the square by adding and subtracting 12

y -3(x^2 -4x +4) =1 +12

-3(x-2)^2 +12 vertex is (2,12) axis of symmetry is x=2

9 y=2x^2-4x-1

y=2(x^2 -2x +1) -1 -2

y=2(x-1)^2 -3 vertex is (1,-3) axis of symmetry is x=1

11 f(x) = 3x^2 -9x +2

= 3(x^2 -3x+ 9/4) +2+ 9/4

=3(x-3/2)^2 + 17/4 vertex is (3/2, 17/4) axis of symmetry is x=3/2

13 f(x) = -5x^2 + 3x + 2

= -5(x^2 -3x/5 +9/100) + 2 +9/100

= -5(x-3x/10)^2 + 2.09 vertex is (0.3, 2.09) axis of symmetry is x=0.3 or 3/10

15 f(x) =6x^2 -6x -5

= 6(x^2 -x + 1/4) -5 -6/4

=6(x-1/2)^2 - 13/2 vertex is (1/2, -13/2) axis of symmetry is x= 1/2