Answer
See below
Work Step by Step
The standard form of the equation is: $y=ax^2+bx+c$
Given three points: $(-1,9)\\(1,1)\\(3,17)$
Substitute: $9=a(-1)^2+b(-1)+c\\1=a(1)^2+b(1)+c\\17=a(3)^2+b(3)+c$
We have the system: $a-b+c=9\\a+b+c=1\\9a+3b+c=17$
Subtract the second equation from the first equation:
$2b=-8\\b=-4$
Substitute $b$ to the first and third equation:
$a+c=5\\9a+c=29$
Multiply the first equation with $-1$ and add to the third equation:
$9(-2)+3(-4)+c=17\\
8a=24\\a=3$
Find $c$:
$3+c=5\\c=2$
Hence, $a=3\\b=-4\\c=2$
Substitute back to the initial equation: $y=3x^2-4x+2$
