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# SLC #27 The Pythagorean Sea

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BC: By: Savannah Costa Algebra and Trig period C 1-6-12 Question 27

FC: Question 27: The Pythagorean Sea | By: Savannah Costa

1: Question 27: The Pythagorean Sea, in South Antarctica has a depth that varies quadratically with its width. The width of the sea is 1000 meters. Two hundred meters from shore, the depth is 20 meters. ~ Define the variables. Write the ordered pairs for this function. (Hint: At sea level the depth is zero.) Explain how you came up with the ordered pairs. ~Find the equation of this function expressing depth in terms of width. ~What is the deepest part of the Pythagorean Sea? ~What is the mathematical name for this point? ~Sketch the graph of this function.

2: Part one: Define the variables. Write the ordered pairs for this function. Explain how you came up with the ordered pairs. | Let Y= Depth Let X= Width Ordered Pairs: 0,0 200,20 800,20 1000,0 | Explanation: The width of the sea is the x axis and the depth pf the is the y axis. The first ordered pair is 0,0. I got this because the depth 0 when the width is 0. I got the next ordered pair of 200,20 because when it is 200 meters from the shore, the depth is 20 meters. I got the next ordered pair of 800,20 because 200 meters from the other side of the lake is 20 meters in depth. Since the sea is 1000 meter in width, 200 meters from one side makes it 800 meters. I got the next ordered pair of 1000,0 because the width of the sea is 1000 meters, and at 1000 meters, the depth is 0.

3: Part two: Find the equation of this function expressing depth in terms of width. | The Equation to this function: y= -.000125x^2 + .125x + 0

4: What is the deepest part of the Pythagorean Sea? | At the width of 500 meters, the deepest part of the Pythagorean Sea is 31.25 meters.

5: What is the mathematical name for this point? | The mathematical name for this point is called the vertex of the parabola.

6: Sketch the graph of this function.

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• By: Savannah C.
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