Explanation Definition used: “The graph of the function f ( x ) = a x 2 + b x + c is a parabola with the following characteristics”. 1. The parabola open upward if a > 0 and downward if a < 0 ; 2. The y − intercept is at ( 0 , c ) ; 3. The x − intercepts , if they exist , occur where f ( x ) = 0 4. The vertex is at ( − b 2 a ) , f ( ( − b 2 a ) ) ; 5. The axis of symmetry is x = − b 2 a . Calculation: The given quadratic equation in the form of a x 2 + b x + c = 0 . Here, the values of a = − 1 4 , b = 1 and c = 2 . The value of a is less than zero thus, the graph of the parabola is opens downward direction. Obtain the y intercepts by substituting x = 0 in the equation y = − 1 4 x 2 + x + 2 . y = − 1 4 ( 0 ) 2 + ( 0 ) + 2 = 2 Therefore, the y intercepts is ( 0 , 2 ) . Substitute y = 0 in the equation y = − 1 4 x 2 + x + 2 to obtain the x intercepts, − 1 4 x 2 + x + 2 = 0 − x 2 + 4 x + 8 = 0 ( ∵ Multiply by 4 both side ) Use quadratic formula to solve the above equation. x = − 4 ± ( 4 ) 2 − 4 ( − 1 ) ( 8 ) 2 ( − 1 ) = − 4 ± 48 − 2 = 2 ± 2 3 Therefore, the x intercepts are x = 2 − 2 3 and x = 2 + 2 3

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 10, Problem 32RE

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Chapter 10 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 10.1 - Find the domain and range for the function y=1x24.Ch. 10.1 - Prob. 2YT Ch. 10.1 - Solve the following. W1.4x2 9 = 0 (Sec. R.4)Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E

Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Which of the following rules define y as a...Ch. 10.1 - Which of the following rules define y as a...Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Give the domain of each function defined as...Ch. 10.1 - Give the domain of each function defined as...Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - In Exercises 38, give the domain and range. 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Prob. 77E Ch. 10.1 - Metabolic Rate The basal metabolic rate (in...Ch. 10.1 - Prob. 79E Ch. 10.1 - Prob. 80E Ch. 10.1 - Prob. 81E Ch. 10.2 - For the function y = 2x2 6x 1, (a) complete the...Ch. 10.2 - Prob. 2YT Ch. 10.2 - Prob. 3YT Ch. 10.2 - Prob. 4YT Ch. 10.2 - Prob. 5YT Ch. 10.2 - Prob. 1WE Ch. 10.2 - Prob. 2WE Ch. 10.2 - Prob. 3WE Ch. 10.2 - Prob. 4WE Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - In Exercise 3-8, match the correct graph A-F to...Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - Prob. 27E Ch. 10.2 - In Exercise, follow the directions for, match the...Ch. 10.2 - 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The function y = − 1 4 x 2 + x + 2 .

Solution Summary: The author illustrates the graph of the function y=-14x2+x+2 in Figure 1.

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Chapter 10 Solutions