Answer:
\(3x^{2}-2x+5\)
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:
\(3x^{2}-2x+5\).
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 \(3x^{2}-2x+5\),
\(3(-2)^{2}-2(-2)+5\)
\(3(4)+4+5\)
=\(21\)
Again, substituting x=-1 in the same equation, we have
\(3(-1)^{2}-2(-1)+5\)
\(3+2+5\)
=\(10\)
Putting x=0,
\(3(0)^{2}-2(0)+5\)
=\(5\)
Putting x=1,
\(3(1)^{2}-2(1)+5\)
=\(6\)
Putting x=2,
\(3(2)^{2}-2(2)+5\)
=13
Hence, the quadratic equation which is represented by the table is \(3x^{2}-2x+5\)
