Question

Write the standard form of the quadratic equation modeled by the points shown in the table below. x -1 0 1 2 3 y -20 -6 2 4 0

Answer 1

We know that
The Standard Form of a Quadratic Equation looks like this
 ax² + bx + c = 0

we have 
x -1    0 1 2 3
y -20 -6 2 4 0

for x=0   y=-6
then
 y=ax² + bx + c -------->  -6=a*0² + b*0 + c ---------> c=-6

for y=0  x=3
then
 y=ax² + bx + c------->  0=a*3² + b*3 -6---------> 9a+3b=6----> equation 1

for x=2  y=4

then

 y=ax² + bx + c-----> 4=a*2² + b*2 -6-----> 4=4a+2b-6-----> 4a+2b=10----> a=2.5-0.5b----> equation 2

 

I substitute 2 in 1

9*[2.5-0.5b]+3b=6------> 22.5-4.5b+3b=6------> 1.5b=16.5------> b=11

a=2.5-0.5*11------> a=2.5-5.5------> a=-3

The Standard Form of a Quadratic Equation is

 ax² + bx + c = 0--------> -3x²+11x-6=0

the answer is

-3x²+11x-6=0

 See the attached figure