$\"\"$

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

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The point has a $\"\"$ -intecept at $\"\"$ and has a slope of $\"\"$ at point $\"\"$ .

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$\"\"$ passes through the function.

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$\"\"$

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$\"\"$ passes through the function.

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$\"\"$

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$\"\"$

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Slope of the function is derivative function at $\"\"$ .

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$\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in the above derivative function.

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$\"\"$

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Hence slope of the tangent line is $\"\"$ .

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The function has a slope of tangent line as $\"\"$ .

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Subtitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$

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Solve the three equations.

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Subtract equation (2) from equation (3).

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$\"\"$

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Subtract equation (4) from equation (1).

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$\"\"$

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Substitute $\"\"$ in the equation (3).

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$\"\"$

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

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in second degree polynomial function.

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$\"\"$ .

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