Question

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

Answer 1

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

Answer 2

Answer:

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

Step-by-step 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 $-3x^2+11x-6$