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The equation is $\"\"$ .

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Since the square term is $\"\"$ , the parabola is horizontal.

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Standard form of the horizontal parabola is $\"\"$ .

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(a)

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Find the standard form of the equation by using completing square method.

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$\"\"$

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$\"\"$

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To change the expression $\"\"$ into a perfect square trinomial add $\"\"$ to each side of the equation.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Standard form of the parabola is $\"\"$ .

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(b)

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The distance the swimmer is from the stern of the boat represents the length of rope needed to attach the swimmer to the stern.

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The stern of the boat is located at vertex of the parabola formed and the swimmer is at the focus.

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Find the vertex and focus.

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$\"\"$

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Rewrite the equation as $\"\"$ .

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Compare the above equation with $\"\"$ .

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Vertex $\"\"$ and $\"\"$ .

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Since $\"\"$ is positive, the parabola opens right.

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Focus $\"\"$ .

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Find the distance between focus and vertex.

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Formula for distance between two points is $\"\"$ .

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$\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Therefore, the length of rope attaching the swimmer to the stern of the boat is $\"\"$ .

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(a) $\"\"$ .

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(b) The length of rope attaching the swimmer to the stern of the boat is $\"\"$ .