Concept explainers
a.
To find: The quadratic function whose graph passes through the given points.
a.
Answer to Problem 89E
The quadratic function whose graph passes through the given points is ,
Explanation of Solution
Given information: The table shows the horizontal distances x and vertical distances y
Of a thrown baseball at three specific times, where x and y are measured in feet.
Horizontal distance, x | Height y |
0 | 5.0 |
15 | 9.6 |
30 | 12.4 |
Calculation:
Given the equation of parabola:
Using the data given, the system of equations is:
Now solving this system of equation
Augmented matrix:
Reducing this augmented matrix in echelon form.
Get a leading 1 in row 1:
Get 0s below the leading 1 in row 1:
Get a leading 1 in row 2:
Write the system of linear equations corresponding to the reduced row-echelon form of the matrix:
Use back-substitution to find a and b .
The equation of the parabola is:
b.
To graph: The quadratic function using the graphing utility and approximate the maximum height of the ball using the graph.
b.
Answer to Problem 89E
Maximum height
Explanation of Solution
Given information: The table shows the horizontal distances x and vertical distances y
Of a thrown baseball at three specific times, where x and y are measured in feet.
Horizontal distance, x | Height y |
0 | 5.0 |
15 | 9.6 |
30 | 12.4 |
Calculation:
Using a graphing utility the graph of the function
From the graph,
Maximum height
Chapter 7 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