Question

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

Answer 1

The required equation is
`-3x^2+11x-6`

Explanation:

Consider the provided table.

As we know the standard form of the quadratic equation is
`y=ax^2+bx+c`

Substitute x=0 and y=-6 in above standard equation.

`-6=a(0)^2+b(0)+c`

`-6=c`

Substitute x=1, y=2 and c=-6 in standard equation.

`2=a(1)^2+b(1)-6`

`2=a+b-6`

`a+b=8`

`a=8-b`

Substitute x=2, y=4 and c=-6 in standard equation.

`4=a(2)^2+b(2)-6`

`4=4a+2b-6`

`4a+2b=10`

`2a+b=5`

Substitute value of a in above equation.

`2(8-b)+b=5`

`16-2b+b=5`

`b=11`

Substitute the value of b in
`a=8-b`

`a=8-11`

`a=-3`

Hence, the required equation is
`-3x^2+11x-6`

Answer 2

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