Assignment Assignment for Lesson 14.1
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1 Assignment Assignment for Lesson.1 Name Date The Origin of Parabolas Parabolas Centered at the Origin 1. Consider the parabola represented by the equation y 2 12x 0. a. Write the equation of the parabola in standard form. b. What are the x-intercept(s) of the parabola? c. What are the y-intercept(s) of the parabola? d. Calculate the coordinates of each point on the parabola that has an x-coordinate of 3. Chapter l Assignments 229
2 e. Use the points from parts (b) through (d) to sketch the parabola on the gird. 2. Consider the graph of the parabola shown with directrix y 1. y y = 1 (0, 0) x a. What are the coordinates of the vertex? b. What is the axis of symmetry? 230 Chapter l Assignments
3 Name Date c. What is the value of p? d. What are the coordinates of the focus? e. Write an equation for the parabola in standard form. Chapter l Assignments 231
4 Determine the following for each parabola. coordinates of the vertex axis of symmetry value of p coordinates of the focus equation of the directrix concavity eccentricity Then, graph and label the parabola. 3. x 2 2y 4. y 2 x Chapter l Assignments
5 Assignment Assignment for Lesson.2 Name Date Up, Down, Left, and Right! Parabolas Not Centered at the Origin Describe the transformation(s) applied to the parabola x 2 y to result in each given parabola. Then identify the vertex of the given parabola. 1. ( x 5) 2 ( y 9) 2. ( x 7) 2 ( y 10) Describe the transformation(s) applied to the parabola y 2 x to result in each given parabola. Then identify the vertex of the given parabola. 3. ( y 6) 2 x 4. ( y 11) 2 ( x 4) Chapter l Assignments 233
6 Determine the following for each parabola. coordinates of the vertex axis of symmetry value of p coordinates of the focus coordinates of the directrix concavity Then, graph and label the parabola. 5. ( y 1) 2 10( x 3) 6. ( x 2) 2 4( y 5) 234 Chapter l Assignments
7 Name Date Write the equation of each parabola given its graph. 7. y = 5 4 y 8. x = 9 16 y ( 4, 1) x = 4 2 ( 4, 3) 4 6 x ( 3, 2) (3, 2) y = 2 4 x x = Chapter l Assignments 235
8 236 Chapter l Assignments
9 Assignment Assignment for Lesson.3 Name Date Graphs, Equations, and Key Characteristics of Parabolas Forms of Parabolas 1. A parabola has a vertex at ( 1, 3) and a focus at (2, 3). a. Write an equation of the parabola in standard form. Show all your work. b. Graph the parabola. Chapter l Assignments 237
10 2. A parabola has a focus at (2, 4.5) and a directrix at y 3.5. a. Write an equation of the hyperbola in standard form. Show all your work. b. Graph the parabola. 3. The equation of a parabola is y 2 y x Write the equation of the parabola in standard form. 238 Chapter l Assignments
11 Name Date 4. The equation of a parabola is ( x 9) 2 15( y 1). Write the equation of the parabola in general form. Write the equation of each parabola in standard form given its graph y y y = 3 x = 7 (7, 7) (7, 5) 4 x = 3.75 x y = 4 ( 3.75, 4) (0, 4) x 20 Chapter l Assignments 239
12 240 Chapter l Assignments
13 Assignment Assignment for Lesson.4 Name Date Satellite Dishes, Radio Dishes, and Archways Parabolas and Problem Solving 1. A home satellite dish is in the shape of a parabola. The parabola that models the dish has a focus that is 10 inches from the vertex and is positioned so that its axis of symmetry is along the y-axis and the vertex is at the origin. a. What are the coordinates of the focus? b. What is the equation of the directrix? c. Write an equation in standard form to model the satellite dish. d. Graph the parabola. Chapter l Assignments 241
14 2. A cable between two towers on the Golden Gate Bridge in San Francisco can be modeled by the equation of a parabola. The distance between the towers is about 4200 feet and the height of each tower is about 500 feet, as shown. 500 ft 4200 ft a. Write three points on the parabola representing the cable if the vertex is at the origin and the axis of symmetry is along the y-axis. b. Use a graphing calculator to determine the equation of the parabola. c. Draw a graph of the equation representing the cable between the towers. 242 Chapter l Assignments
15 d. Write the equation of the parabola in standard form. What is the value of p? e. Determine the coordinates of the focus of the parabola representing the cable. Chapter l Assignments 243
16 244 Chapter l Assignments
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