Answer:
The required equation is [tex]-3x^2+11x-6[/tex]
Step-by-step explanation:
Consider the provided table.
As we know the standard form of the quadratic equation is [tex]y=ax^2+bx+c[/tex]
Substitute x=0 and y=-6 in above standard equation.
[tex]-6=a(0)^2+b(0)+c[/tex]
[tex]-6=c[/tex]
Substitute x=1, y=2 and c=-6 in standard equation.
[tex]2=a(1)^2+b(1)-6[/tex]
[tex]2=a+b-6[/tex]
[tex]a+b=8[/tex]
[tex]a=8-b[/tex]
Substitute x=2, y=4 and c=-6 in standard equation.
[tex]4=a(2)^2+b(2)-6[/tex]
[tex]4=4a+2b-6[/tex]
[tex]4a+2b=10[/tex]
[tex]2a+b=5[/tex]
Substitute value of a in above equation.
[tex]2(8-b)+b=5[/tex]
[tex]16-2b+b=5[/tex]
[tex]b=11[/tex]
Substitute the value of b in [tex]a=8-b[/tex]
[tex]a=8-11[/tex]
[tex]a=-3[/tex]
Hence, the required equation is [tex]-3x^2+11x-6[/tex]
