Concept explainers
To write:The equation of parabola in standard form, whose graph is given, and verify the result using graphing utility.
Answer to Problem 33E
The standard equation of the graphed parabola is
Explanation of Solution
Given data:
The graph of the parabola is shown in Figure-1 here.
Concept used:
Everyquadratic function represents a parabola. Thestandard form of quadratic function
Calculations:
Let the quadratic function
As the point
As the point
As the point
Now, subtracting equation (2) from equation (3)
Now, subtracting equation (2) from equation (1)
From equation (3)
(Substituting values of a&b)
Thus, the equation of the graphed parabola is
The quadratic function that represents given parabola is
Equation (4) is the required standard form of the parabola.
Now, comparing equation (1) with the function
Thus, the quadratic function
Since,
The graph of the function
We observe that the graph of function
Conclusion:
The standard equation of the graphed parabola is
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning