Explanation There are number of ways to write the quadratic equation a x 2 + b x + c . The value of a defines the opening shape of the function. 1. If the function is written in standard form - a x 2 + b x + c , then the y-intercept is given by c . 2. If the function is written in the factored form - f ( x ) = a ( x - r ) ( x - s ) , then x-intercept is given by r and s . 3. If the function is written in vertex form - y = a ( x - h ) 2 + k , then the coordinates of the vertex is given by ( h , k ) . If the value of a is positive, the minimum value of function is at k and if the value of a is negative, then the maximum value of function is at k . Given: Quadratic function is given as x 2 + 3 x + 3 Formula used: Rewrite the quadratic function in vertex form in order to find the maximum value of the function. Calculation: Function is given as x 2 + 3 x + 3 On adding and subtracting 9 4 inside the parenthesis, we get x 2 + 3 x + 9 4 - 9 4 + 3 On regrouping to complete square, we get [ x 2 + 3 x + 9 4 - 9 4 ]

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1, Problem 32CRE

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That the value of quadratic function x2+ 3x + 3 is always greater than or equal to zero for all values of x

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Chapter 1, Problem 31CRE

Chapter 1, Problem 33CRE

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Chapter 1 Solutions

Calculus - Standalone book

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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That the value of quadratic function x 2 + 3 x + 3 is always greater than or equal to zero for all values of x

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That the value of quadratic function x2+ 3x + 3 is always greater than or equal to zero for all values of x

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