Concept explainers
For Exercises 27—34, an equation of a parabola
- Identify the vertex, value of p, focus, and focal diameter of the parabola.
- Identify the endpoints of the laths rectum.
- Graph the parabola.
- Write equations for the directrix and axis of symmetry. (See Examples 4)
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
ALEKS AC COLLEGE ALGB & TRIG
Additional Math Textbook Solutions
Algebra and Trigonometry
Algebra and Trigonometry (6th Edition)
A Graphical Approach to College Algebra (6th Edition)
Linear Algebra with Applications (2-Download)
Glencoe Algebra 2 Student Edition C2014
High School Math 2012 Common-core Algebra 1 Practice And Problem Solvingworkbook Grade 8/9
- Exercises 45–48 give equations for parabolas and tell how many units up or down and to the right or left each parabola is to be shifted. Find an equation for the new parabola, and find the new vertex, focus, and directrix. 45. y2 = 4x, 46. x2 = 8y, right 1, down 7 47. x2 = 6y, left 2, down 3 48. y2 = -12x, right 4, up 3 left 3, down 2arrow_forwardExercises 45–48 give equations for parabolas and tell how many units up or down and to the right or left each parabola is to be shifted. Find an equation for the new parabola, and find the new vertex, focus, and directrix.arrow_forwardIn Exercises 3–10, describe the curve represented by each equation. Identify the type of curve and its center (or vertex if it is a parabola). Sketch each curve.arrow_forward
- For Exercises 67–70, identify the equation as representing an ellipse or a hyperbola, and match the equation with the graph. (x – 5)² 67. (y + 2)² = 1 (x – 5)? 68. (y + 2)? = 1 49 36 36 49 (x - 5)? 69. (y + 2)² = 1 (y + 2)² = 1 (x - 5)? 49 36 70. 49 36 А. В. С. D. 15 12 41 6 -6-4-2 4 6 8 10 12 14 4 6 8 10 12 14 -6 -4 2. 4 6 8 10l 12 14 -6 1k 15 18 21 -6arrow_forwardFor Exercises 43–48, the equation represents a conic section (nondegenerative case). a. Identify the type of conic section. (See Example 6) b. Graph the equation on a graphing utility. 43. 4x – 4xy + 5y – 20 = 0 44. 6x + 4V3xy + 2y - 18x + 18V3y – 72 = 0 45. 2x – 6xy + 3y² - 4x + 12y – 9 = 0 46. 5x – 3xy + 2y – 6 = 0 47. 4x + 8xy + 4y – 2x – 5y – 2 = 0 48. 4x? + 8V3xy + 3y + 2x – 12y – 6 = 0arrow_forwardIn Exercises 11–16, find the vertex, focus, and directrix of the parabola, and sketch its graph.arrow_forward
- Find the equation y = ax2 + bx +c of the parabola that passes through the points (-2,0), (0, –14), (7,0) .arrow_forwardExercises 27–34 give equations for hyperbolas. Put each equation instandard form and find the hyperbola’s asymptotes. Then sketch thehyperbola. Include the asymptotes and foci in your sketch.27. x2 - y2 = 1 28. 9x2 - 16y2 = 14429. y2 - x2 = 8 30. y2 - x2 = 431. 8x2 - 2y2 = 16 32. y2 - 3x2 = 333. 8y2 - 2x2 = 16 34. 64x2 - 36y2 = 2304arrow_forward3. graph the parabola Y = 3(x - 2)2 + 1. plot five points on the parabola.arrow_forward
- 2. Obtain the graph of the parabola y = -x² + 4x using transformations of the graph of y = x². Explain each step.arrow_forwardFind the equation of the parabola whose axis is parallel to the x-axis and passes through the points (3,1), (0,0), and (8,-4).arrow_forwardWrite an equation for a parabola with a vertex of (5,2) and a focus of (5,1) in vertex form. Show all of your work.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage