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Option D: is the function
Explanation:
Let the general form of quadratic equation be
The function passes through the intercepts and
and also passes though the point
Substituting the points ,
and
in the equation
, we get,
-----------(1)
----------(2)
-----------(3)
Subtracting (1) and (2), we get,
-----------(4)
Subtracting (2) and (3), we get,
------------(5)
Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,
Thus, the value of a is
Substituting in equation (4), we get,
Thus, the value of b is
Now, substituting the value of a and b in equation (1), we have,
Thus, the value of c is
Now, substituting the value of a,b and c in the general formula , we get,
Taking out the common term as -2 we get,
Factoring , we get,
Thus, the function is