Superlesson
Project 5-1
Advanced Algebra
Chapter 5, Quadratic Functions and Relations
To see the light emitted by astronomical objects, astronomers use telescopes in the familiar telescope shape. To "see" the radio waves emitted by such objects, astronomers use radio telescopes in the shape of a parabola.
Part B, Sketching Parabolas: f (x) = ax2
1. During the 1960s, NASA built radio telescopes around the world to study deep space and to track Apollo moon missions.
a. Look at this Photo of a telescope found at the Second Deep Space Station in Spain. Sketch the parabolic radio dish on a coordinate axes with the parabola opening upward and the vertex at the origin OR print the photo and draw a coordinate axis on the photo with the parabola opening upward and the vertex at the origin.
b. The size given for the telescope is the diameter of the dish. Use this value to estimate the depth of the dish. Identify two points on the graph of the parabola, in addition to the origin.c. Estimate the x-value (s) of the point (s) on the graph with a y- value of 3.
d. Find the equation of the parabola.
Part C, Translations: f(x) = a(x h)2 + k
2. Study the photos of New Mexico's Very Large Array (VLA) of radio telescopes.
a.Estimate the depth of each dish.
b. In the photo of the dishes in "Y-formation" estimate the distance between two dishes at the far right.
c. Sketch a VLA dish opening upward with its vertex at the origin. To its right, at the distance you estimated in b, sketch a second dish with its origin on the x-axis.
d. Suppose the equation of the first dish is y = ax2. What is the equation of the second dish?
Part D, Completing the Square
3. Find and study the photo of the 64-Meter Antenna at Parkes, Australia.
a. Sketch the radio telescope, including the tower that holds it, on an xy -coordinate axes. Show the dish in vertical position (the parabola opening upward). Place the base of the tower on thex-axis, centered at the origin.
b. Find the equation of the dish. Write the equation in both standard quadratic form and completed-square form.
Part E, Making Connections
4. Study the picture of the radio telescope at the following Web site.
a. Sketch the Effelsberg radio telescope. Include in your sketch the tall structure that stands in the middle of the dish.
b. On your sketch, show the paths of at least four incoming radio waves.
