急 ! concept of a function

11. C1: y=4x^2

C2: y=4(x-3)^2
C2: y=4(x^2-6x+9)
C2: y=4x^2-24x+36

C3:y+2=4(x-3)^2
C3: y+2=4x^2-24x+36
C3: y=4x^2-24x+34

9. sub (0,22) into y=2(a-x)^2+b
22=2(a-0)^+b
22=2a^2+b..............(1)

when x=a, y is the minimum vertex
now the vertex is (3, c)
a=3, y=c
y=2(a-a)^2+b
c=b

sub a=3 into (1)
22=2(9)+b
22=18+b
b=4
c=b
c=4
the answer is a=3, b=4, c=4

10. sub (2,0) into y=-2(x+a)^2+b
0=-2(2+a)^2+b.............(1)

when x=-a, (-a, y) is the maximum vertex
now y=8 is the maximum
sub (-a, 8) into the equation
8=-2(-a+a)^2+b
b=8
sub b=8 into (1)
0=-2(2+a)^2+8
-8/-2=(2+a)^2
4=(2+a)^2
2+a= 2 or -2
a=0 or -4

find (0,c)
sub a=0, x=0 into equation
c=-2(0+0)^2+8
c=8 (rejected, c is negative)
so a≠0

find (0,c)
sub a=-4, x=0 into equation
c=-2(0+4)^2+8
c=-32+8
c=-24
the answer is a=-4, b=8, c=-24