$\"\"$

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The area of a region bounded by a parabola and a horizontal line is $\"\"$ .

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Where $\"\"$ represents base of the region along the horizantal line.

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$\"\"$ represents height of the region.

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$\"\"$ represents the parabola.

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$\"\"$ represents the horizantal line.

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The points are $\"\"$ and $\"\"$ .

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$\"\"$ .

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Now the base $\"\"$ of the parabola lies on the $\"\"$ axis which calculated by solving $\"\"$ .

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The function $\"\"$ has zeros at $\"\"$ and $\"\"$ .

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Therefore $\"\"$ and $\"\"$ are the factors of $\"\"$ .

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Since the graph has one turning point and it is a parabola $\"\"$ is a quadratic.

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$\"\"$

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The function can be written as $\"\"$ .

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$\"\"$

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Check the points $\"\"$ and $\"\"$ by subustituting the values in the obtained equation.

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$\"\"$ .

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Check for values $\"\"$ .

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$\"\"$

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Check for values $\"\"$ .

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$\"\"$

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Therefore $\"\"$ .

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$\"\"$

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$\"\"$ .

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The function is in the form of $\"\"$ .

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Where $\"\"$

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The vertex is of $\"\"$ is located at the point with the $\"\"$ coordinate, $\"\"$ .

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$\"\"$

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Subustiute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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The vertex of $\"\"$ is at $\"\"$ .

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The distance from the vertex to the horizontal line is the height of the region.

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Therefore height $\"\"$ is

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$\"\"$

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Therefore base $\"\"$ is $\"\"$ .

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Height $\"\"$ is $\"\"$ .

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Subustiute these values in the area of the parabola $\"\"$ .

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$\"\"$

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Therefore area bounded by $\"\"$ and $\"\"$ is $\"\"$ sq.units

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$\"\"$

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Area bounded by $\"\"$ and $\"\"$ is $\"\"$ sq.units.