Concept explainers
To find the Vertex, Focus and Directrix of a parabola.
Answer to Problem 69E
The values of
Explanation of Solution
Given information:
The equation is
Calculation:
The Vertex, Focus and Directrix of a parabola can be obtained as
First convert the equation to standard form by completing the square.
The standard form of the equation of a parabola with vertex at is
Comparing the given equation to the standard form of the equation it can observed that the vertex is
Add to find the focus
Subtract to find the directrix
Because p is negative, the parabola opens negative side of x-axis and the vertex of the parabola will be at and the focus is at
So, the graph is obtained as:
Hence,
The values of
To verify the above graph, use graphing calculator to graph the given equation follow the steps given below:
Step 1: Press WINDOW button to access the Window editor.
Step 2: Press button.
Step 3: Enter the expression which is required to graph.
Step 4: Press GRAPH button to graph the function and adjust the windows according to the graph.
The graph is obtained as:
Hence, the graph is verified.
Chapter 9 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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