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

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 11.1, Problem 9YT

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 8YT

Chapter 11.1, Problem 10YT

Students have asked these similar questions

How to solve 2542000/64132 without a calculator?

How much is the circumference of a circle whose diameter is 7 feet?C =π d

How to solve 2542/64.132

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

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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

Want to see the full answer?

Chapter 11 Solutions