Write the standard form of the quadratic equation modeled by the points shown in the table below.

We know that

The Standard Form of a Quadratic Equation is
 ax² + bx + c = 0

then 
for x=0    y=-6
 a*0² + b*0 + c = -6> c=-6

for x=1    y=2
 a*1² + b*1 -6 = 2> a+b=8> a=8-b> equation 1

for x=3    y=-0
 a*3² + b*3 -6 = 0> 9a+3b=6> equation 2

substituting 1 in 2
9*(8-b)+3b=6> 72-9b+3b=6> 6b=66> b=11
a=8-11> a=-3
so
a=-3
b=11
c=-6
Standard Form of a Quadratic Equation is
 -3x² + 11x - 6 = 0

the answer is
 -3x² + 11x - 6 = 0