Explanation The graph of the function f ( x ) = a x 2 + b x + c is a parabola with the following characteristics. 1. The parabola opens 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 a = − 3 , b = − 6 and c = 4 . Since the value of a is less than zero, the graph of the parabola opens downward direction. Now, find the y intercepts by substituting x = 0 in the above function. y = − 3 x 2 − 6 x + 4 = − 3 ( 0 ) 2 − 6 ( 0 ) + 4 = 4 Therefore, the value of y intercepts is ( 0 , 4 ) . Obtain the x intercepts of the equation y = − 3 x 2 − 6 x + 4 by substituting y = 0 . y = − 3 x 2 − 6 x + 4 0 = − 3 x 2 − 6 x + 4 Use quadratic formula to solve the above equation. x = − b ± b 2 − 4 a c 2 a x = 6 ± 36 + 48 2 ( − 3 ) = 6 ± 84 − 6 On further simplification, 0 = 6 ± 2 21 − 6 = − 1 ± 21 3 x = − 1 + 21 3 and − 1 − 21 3 Therefore, the x intercepts are x = − 1 + 21 3 and x = − 1 − 21 3

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

10th Edition

ISBN: 9780133935592

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

Publisher: PEARSON

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Chapter 10.2, Problem 16E

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To sketch: The parabola y=−3x2−6x+4 and find the vertex, axis of symmetry, x-intercepts and y-intercepts.

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Chapter 10.2, Problem 15E

Chapter 10.2, Problem 17E

Chapter 10 Solutions

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (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. Then,...Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Let f(x) = 6x2 2 and g(x) = x2 2x + 5 to find...Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - For each function defined as follows, find (a) f(x...Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Decide whether each graph represents a function....Ch. 10.1 - Prob. 59E Ch. 10.1 - Prob. 60E Ch. 10.1 - Prob. 61E Ch. 10.1 - Prob. 62E Ch. 10.1 - Prob. 63E Ch. 10.1 - Prob. 64E Ch. 10.1 - Prob. 65E Ch. 10.1 - Prob. 66E Ch. 10.1 - Prob. 67E Ch. 10.1 - Prob. 68E Ch. 10.1 - Prob. 69E Ch. 10.1 - Prob. 70E Ch. 10.1 - Prob. 71E Ch. 10.1 - Prob. 72E Ch. 10.1 - Prob. 73E Ch. 10.1 - Prob. 74E Ch. 10.1 - Attorney Fees According to Massachusetts State...Ch. 10.1 - Tax Rates In New York state in 2014, the income...Ch. 10.1 - 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Prob. 72E Ch. 10.3 - Graph f(x) = 64 x6.Ch. 10.3 - Prob. 2YT Ch. 10.3 - Prob. 1WE Ch. 10.3 - Prob. 2WE Ch. 10.3 - Prob. 3WE Ch. 10.3 - Prob. 4WE Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10.3 - Find any horizontal and vertical asymptotes and...Ch. 10.3 - Prob. 36E Ch. 10.3 - Prob. 37E Ch. 10.3 - Prob. 38E Ch. 10.3 - Prob. 39E Ch. 10.3 - 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The parabola y = − 3 x 2 − 6 x + 4 and find the vertex, axis of symmetry, x -intercepts and y- intercepts.

Solution Summary: The author explains that the graph of the function f(x)=a+bx+c is a parabola with the following characteristics.

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To sketch: The parabola y=−3x2−6x+4 and find the vertex, axis of symmetry, x-intercepts and y-intercepts.

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Chapter 10 Solutions