Answer
See below
Work Step by Step
The standard form of the equation is: $y=ax^2+bx+c$
Given three points: $(2,-1)\\(4,-3)\\(1,-6)$
Substitute: $-1=a(2)^2+b(2)+c\\-6=a(1)^2+b(1)+c\\-3=a(4)^2+b(4)+c$
We have the system: $4a+2b+c=-1\\a+b+c=-6\\16a+4b+c=-3$
Multiply the second equation by $-1$ and add it to the first. Multiply the second equation by $-1$ and add it to the third. We have the new system:
$3a+b=5\\a+b+c=-5\\15a+3b=3$
Hence, $a=-2\\b=11\\c=-15$
Substitute back to the initial equation: $y=-2x^2+11x-15$
