Concept explainers
a.
To find: the equations of the parabolas.
a.
Answer to Problem 51E
The equations of parabolasare
Explanation of Solution
The equations of parabolasare
Given information:
Directrix
Calculation: from the given directrix it can be observed that the parabola has vertical axis.
So the equation of parabola should be in the following form,
For parabola with verticalaxis, directrix is
To comparing the directrix it can be observed that,
So the equation of parabola is,
Hence, the equation of parabola is
b.
To graph the parabolas using graphing device.
b.
Explanation of Solution
Given information: Use graphing device to graph the parabola
Graph: to draw the graph using a graphing device, it is needed to solve equation for y.
To obtain the graph of the parabola, graph the following functions,
Sketch the graph using graphing utility.
Step 1: Press WINDOW button to access the Window editor.
Step 2: Press
Step 3: Enter the expression
Step 4: Press GRAPH button to graph the function.
The graph is obtained as:
Interpretation:
From the above graph, it can be observed that when value of p increases the graph of parabolas stretch.
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning