Explanation There are a 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 a function is written in the standard form - a x 2 + b x + c , then the y-intercept is given by c . 2. If a 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 function is written in the vertex form - y = a ( x - h ) 2 + k , then the coordinates of the vertex are given by ( h , k ) . If the value of a is positive, the minimum value of the function is at k and if the value of a is negative, then the maximum value of function is at k . Given: f ( x ) is given as the square of the distance from point ( 2 , 1 ) to a point ( x , 3 x + 2 ) on the line y = 3 x + 2 Formula Used: 1. Distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given using formula ( x 1 – x 2 ) 2 + ( y 1 − y 2 ) 2 . 2. Rewrite the quadratic function in vertex form in order to find the maximum value of the function. Calculation: Two points are given as ( 2 , 1 ) and ( x , 3 x + 2 ) Distance between ( 2 , 1 ) and ( x , 3 x + 2 ) is given as ( x – 2 ) 2 + ( 3 x + 2 - 1 ) 2 ( x – 2 ) 2 + ( 3 x + 1 ) 2 Now, f ( x ) is given as the square of the distance from point ( 2 , 1 ) to a point ( x , 3 x + 2 ) Thus, f ( x ) = [ ( x – 2 ) 2 + ( 3 x + 1 ) 2 ]

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ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1, Problem 33CRE

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The completion of the square of the function f(x), where f(x) is given as the square of the distance from point (2, 1) to a point (x, 3x + 2) on the line y = 3x + 2 and also find the minimum value of the function f(x).

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Chapter 1, Problem 32CRE

Chapter 1, Problem 34CRE

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Chapter 1 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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The completion of the square of the function f ( x ) , where f ( x ) is given as the square of the distance from point ( 2 , 1 ) to a point ( x , 3 x + 2 ) on the line y = 3 x + 2 and also find the minimum value of the function f ( x ) .

Solution Summary: The author explains how the quadratic equation a defines the opening shape of the function.

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The completion of the square of the function f(x), where f(x) is given as the square of the distance from point (2, 1) to a point (x, 3x + 2) on the line y = 3x + 2 and also find the minimum value of the function f(x).

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Chapter 1 Solutions