$\"\"$

\

(a)

\

The second degree polynomial function P having $\"\"$ , $\"\"$ and $\"\"$ .

\

Let the second degree polynomial of the form $\"\"$ .

\

We have $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ (1)

\

$\"\"$

\

$\"\"$ .

\

Differentiate on each side with respect to $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

We have $\"\"$ .

\

$\"\"$

\

$\"\"$ (2)

\

$\"\"$

\

$\"\"$ .

\

Differentiate on each side with respect to $\"\"$ .

\

$\"\"$

\

We have $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ (3)

\

Solve equations (1), (2) and (3) to find $\"\"$ and $\"\"$ values.

\

Substitute $\"\"$ in equation (2).

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in equation (1).

\

$\"\"$

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

\

The second degree polynomial is $\"\"$ .