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The equation is $\"\"$ .

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Since the $\"\"$ -term is squared, the parabola is vertical.

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Standard form of the vertical parabola is $\"\"$ ,

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where $\"\"$ is vertex.

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

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$\"\"$

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Here $\"\"$ coefficient is $\"\"$ , for perfect square make $\"\"$ coefficient $\"\"$ by dividing each side by $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$ .

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Add $\"\"$ on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Standard form is $\"\"$ .

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(b)

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Maximum height that a hot dog can reach at the vertex of the parabola.

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Find the vertex.

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

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Compare with $\"\"$ .

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Vertex $\"\"$

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Therefore, the maximum height $\"\"$ feet.

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(a) $\"\"$ .

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(b) The maximum height $\"\"$ feet.