Concept explainers
To find: The expressions for the given quadratic graphs.
Answer to Problem 8E
The expression of the graph f is
The expression of the graph g is
Explanation of Solution
Consider the graph of the function f.
Here, the graph represents that an open upward parabola with vertex (3, 0). Moreover, it is observed that the point (4, 2) is lies on the parabola.
The general equation of the open upward parabola is,
Substitute
Thus, the equation of the parabola with vertex (0, 3) is
That is,
Consider the graph of the function g.
Here, the graph represents that an open downward parabola which passing through the points (−2, 2), (0, 1) and (1, −2.5).
The general form of the
Substitute the points (−2, 2) and (1, −2.5) in equation (2) and obtain the equations as given below.
If (x, y) = (−2, 2), then the equation is
If (x, y) = (0, 1), then the equation is
Add the equations (3) and (4) and find the value of a.
Substitute
Thus, the equation of the graph g is
Substitute
That is,
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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