Understanding Paraboloid Satellite Dishes

The video tutorial explains how a satellite dish is shaped like a paraboloid of revolution, formed by rotating a parabola around its axis of symmetry. The receiver is located at the focus. The tutorial derives the equation of the parabola representing the dish, using given dimensions, and calculates the focus's location. The parabola's vertex and intercepts are used to find the equation, and the focus is determined to be 36 feet above the vertex.

What shape is a satellite dish described as in the video?

• Paraboloid of Revolution

• Cylinder

• Cone

• Sphere

How wide is the satellite dish across its opening?

• 18 ft

• 9 ft

• 72 ft

• 36 ft

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the depth of the satellite dish at its center?

• 72 ft

• 9 ft

• 18 ft

• 36 ft

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CCSS.HSF-IF.C.7A

What is the vertex of the parabola representing the satellite dish?

• (9, 0)

• (0, 0)

• (0, 9)

• (36, 0)

What is the general form of the equation used for the parabola?

• y = ax^2 + bx + c

• x^2 = 4p(y - k)

• y^2 = 4p(x - h)

• x = ay^2 + by + c

Which x-intercept is used to find the value of 'p'?

• (0, 0)

• (9, 0)

• (36, 0)

• (0, 9)

What is the value of 4p in the equation of the parabola?

• 9

• 144

• 72

• 36

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CCSS.3.MD.D.8

What is the calculated value of 'p'?

• 9

• 72

• 18

• 36

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CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Where is the receiver located in relation to the vertex?

• At the vertex

• 72 ft above the vertex

• 36 ft above the vertex

• 9 ft below the vertex

What is the ordered pair for the focus of the parabola?

• (36, 0)

• (0, 36)

• (0, 9)

• (0, 27)