Answer:
This is a tricky problem, don't feel bad for not knowing this :/ I think this is too much in one question even :P I'll give you the answers and how to get them but really it's going to be a lot to understand in one try. Pay attention :P
Step-by-step explanation:
first graph the given table .. I use Desmos b/c it's handy
we want y = A[tex]x^{2}[/tex] + bx + c
given 1st 2nd
5 -5 2
0 -3 2
-3 -1 2
-4 1 2
-3 3 2
0 5 2
5 7
12
A=2nd / 2 = 2/2 = 1
B=?
C= 5
x=1
y=12
y = a[tex]x^{2}[/tex] + bx +c
12=[tex]1^{2}[/tex] + b(1) +5
12=1+ b +5
6=b :)
y = [tex]x^{2}[/tex] + 6x +5 ( the answer to a) in the question )
factor it
(x+5)(x+1) ( answer to b) in the question
vertex form
y = a(x-h)2 + k
where h = −b/2a
and k = f( h )
h=6/2(1) = 3
k = [tex]3^{2}[/tex] + 6(3) +5
k=32
y =x-3 + 32 ( answer to c) in question )
let me know if this worked for you :) ( I did this fast late at night :/ )
