$\"\"$

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The function $\"\"$ .

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Change $\"image\"$ to $\"image\"$ .

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$\"\"$

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The function is half an ellipse.

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Convert the above equation in standard form of ellipse.

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$\"\"$

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Square on both sides.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Compare it to standard form of vertical ellipse $\"\"$ (Center at origin)

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Where $\"\"$ .

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$\"\"$ is length of semi major axis and $\"\"$ is semi minor axis.

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In this case $\"\"$ , center at $\"image\"$ .

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Major axis length is 8 units and minor axis length is 4 units.

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$\"\"$

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Graph:

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Draw the coordinate plane.

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Plot the center at $\"\"$ .

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The function is square root function. So negative $\"\"$ values is not possible.

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Draw the minor axis and positive part of major axis.

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Sketch the top part of ellipse in first and second quadrants only.

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$\"\"$

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Observe the graph: The $\"image\"$ -intercepts are $\"\"$ and $\"image\"$ -intercept is $\"\"$ .

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$\"\"$

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The $\"image\"$ -intercepts are $\"\"$ and $\"image\"$ -intercept is $\"\"$ .