Answer
See below
Work Step by Step
The standard form of the equation is: $y=ax^2+bx+c$
Given three points: $(-1,-1)\\(1,11)\\(3,7)$
Substitute: $-1=a(-1)^2+b(-1)+c\\11=a(1)^2+b(1)+c\\7=a(3)^2+b(3)+c$
We have the system: $a-b+c=-1\\a+b+c=11\\9a+3b+c=7$
Subtract the second equation from the first equation:
$2b=12\\b=6$
Substitute $b$ to the second and third equation:
$a+c=5\\9a+c=-11$
Subtract the two equations to find $a$:
$-8a=16\\
a=-2$
Find $c$:
$(-2)+6+c=11\\c=7$
Hence, $a=-2\\b=6\\c=7$
Substitute back to the initial equation: $y=-2x^2+6x+7$
