Answer:
[tex]3x^{2}-2x+5[/tex]
Step-by-step explanation:
The value for each value of x is given by f(x) in the table, the quadratic equation which satisfies all the values f(x) at each value of x is given by:
[tex]3x^{2}-2x+5[/tex].
This can be found by substituting all the values of x in the equation and check whether it satisfies the corresponding value f(x) or not.
Therefore, substituting x=-2 in the quadratic equation [tex]3x^{2}-2x+5[/tex],
[tex]3(-2)^{2}-2(-2)+5[/tex]
[tex]3(4)+4+5[/tex]
=[tex]21[/tex]
Again, substituting x=-1 in the same equation, we have
[tex]3(-1)^{2}-2(-1)+5[/tex]
[tex]3+2+5[/tex]
=[tex]10[/tex]
Putting x=0,
[tex]3(0)^{2}-2(0)+5[/tex]
=[tex]5[/tex]
Putting x=1,
[tex]3(1)^{2}-2(1)+5[/tex]
=[tex]6[/tex]
Putting x=2,
[tex]3(2)^{2}-2(2)+5[/tex]
=13
Hence, the quadratic equation which is represented by the table is [tex]3x^{2}-2x+5[/tex]
