f.4 mathz...about functions and graphs

a)
f(1)=1^2+a+b
0=1+a+b
a+b=-1
f(2)=2^2+2a+b
5=4+2a+b
2a+b=1

a+b=-1...(1)
2a+b=1...(2)

from(1),a=-1-b...(3)
sub (3) into (2),
2(-1-b)+b=1
-2-2b+b=1
-b=3
b=3

sub b=3 into (1),
a+3=-1
a=-4

so,a=-4,b=3

b)
f(3)=3^2+3a+b
f(3)=9+3(-4)+3
f(3)=9-12+3
f(3)=0

f(-3)=(-3)^2-3a+b
f(-3)=9-3(-4)+3
f(-3)=9+12+3
f(-3)=24

f(3)-f(-3)=0-24
f(3)-f(-3)=-24

a) f(x)=x^2+ax+b
f(1)=(1)^2+a(1)+b
=a+b+1
f(2)=(2)^2+a(2)+b
=2a+b+4
a+b+1=0
a=-(b+1)
2a+b+4=5
a=(1-b)/2
-(b+1)=(1-b)/2
2b+2=b-1
b=-3
a=2
b)f(3)-f(-3)
(3)^2+a(3)+b-[(-3)^2+a(-3)+b]
=9+3a+b-9+3a-b
=6a
=12