Answer:
[tex]y=-4x^{2} +7x+6\\[/tex]
Step-by-step explanation:
[tex]y=ax^{2} +bx+c\\[/tex]
Points are (1,9), (2,4), and (4,-30).
[tex]\\9=a+b+c\\4=4a+2b+c\\-30=16a+4b+c\\[/tex]
Subtract the first from the second.
-5 = 3a+b
Subtract 4 times the second from the third.
-34=12a+2b
-14=-2b
b=7
a=-4
c=6