Explanation Given Information: The provided function is, f ( x ) = x 2 + 4 x + 1 Formula used: Perform following steps to find the x -intercept of the quadratic function f ( x ) = a x 2 + b x + c : Step 1: Substitute f ( x ) = 0 . Step 2: Add/subtract constant term from both sides. Step 3: Completing the square by adding ( 1 2 ⋅ coefficient of x ) 2 on both sides. Step 4: Factories and simplify. Step 5: Use principle of square roots as: If x 2 = a Then, x = a or x = − a Step 6: Draw graph of the function. Step 6: Check the answer by substituting it in the original equation. Calculation: Consider the provided function, f ( x ) = x 2 + 4 x + 1 Substitute f ( x ) = 0 : x 2 + 4 x + 1 = 0 Subtract 1 from both sides: x 2 + 4 x + 1 − 1 = 0 − 1 x 2 + 4 x = − 1 As, the coefficient of x is 4, Substitute coefficient of x = 4 in ( 1 2 ⋅ coefficient of x ) 2 : ( 1 2 ⋅ 4 ) 2 = ( 2 ) 2 = 4 Add 4 on both sides of equation, x 2 + 4 x = − 1 and solve to make it a complete square: x 2 + 4 x + 4 = − 1 + 4 x 2 + 2 ⋅ 2 ⋅ x + 2 2 = 3 ( x + 2 ) 2 = 3 By using the principle of square roots, apply square root on both sides: ( x + 2 ) 2 = ± 3 x + 2 = ± 3 Subtract 2 from both sides: x + 2 − 2 = − 2 ± 3 x = − 2 ± 3 Thus, x = − 2 + 3 and x = − 2 − 3 Graph: Now, draw the graph of the function, f ( x ) = x 2 + 4 x + 1 Substitute x = − 6 in f ( x ) = x 2 + 4 x + 1 : f ( − 6 ) = ( − 6 ) 2 + 4 ( − 6 ) + 1 = 36 − 24 + 1 = 13 Substitute x = − 2 in f ( x ) = x 2 + 4 x + 1 : f ( − 6 ) = ( − 2 ) 2 + 4 ( − 2 ) + 1 = 4 − 8 + 1 = − 3 Substitute x = 0 in f ( x ) = x 2 + 4 x + 1 : f ( 0 ) = ( 0 ) 2 + 4 ( 0 ) + 1 = 0 − 0 + 1 = 1 Substitute x = 2 in f ( x ) = x 2 + 4 x + 1 : f ( 2 ) = ( 2 ) 2 + 4 ( 2 ) + 1 = 4 + 8 + 1 = 13 Now, draw the table of above observations for f ( x ) = x 2 + 4 x + 1 : x − 6 − 2 0 2 f ( x ) 13 − 3 1 13 Graph of above table for f ( x ) = x 2 + 4 x + 1 :

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

7th Edition

ISBN: 9780134462707

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

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Chapter 11.1, Problem 9YT

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To calculate: The x-intercepts of the graph of f(x)=x2+4x+1.

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Chapter 11.1, Problem 8YT

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Chapter 11 Solutions

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

Ch. 11.1 - Solve: 64=y2.Ch. 11.1 - Solve: t2=10. Give exact solutions and...Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 5YT Ch. 11.1 - 6. Solve: . Ch. 11.1 - Prob. 7YT Ch. 11.1 - Prob. 8YT Ch. 11.1 - Prob. 9YT Ch. 11.1 - Prob. 10YT

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The x -intercepts of the graph of f ( x ) = x 2 + 4 x + 1 .

Solution Summary: The author explains how to calculate the x -intercepts of the quadratic function f(x) = 2+4x+1.

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To calculate: The x-intercepts of the graph of f(x)=x2+4x+1.

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