Answer:
Step-by-step explanation:
Let A=ax²+bx+c
x=1,A=a+b+c or 7=a+b+c ...(1)
x=2,A=4a+2b+c or 12=4a+2b+c ...(2)
x=3,A=9a+3b+c or 15=9a+3b+c ...(3)
subtract (1) from (2) & (3)
3a+b=5 ...(4)
8=8a+2b
or 4a+b=4 ...(5)
subtract (4) from (5)
a=-1
from (4)
-3+b=5
b=5+3=8
b=8
from (1)
-1+8+c=7
c=0
so A=-x²+8x
thus table shows it is quadratic.
b.
A=-x²+8x=-(x²-8x+16-16)
or A=-(x-4)²+16
vertex is (4,16)
