How to Find the Vertex of f(x)=x^2+4x+1 | Step-by-Step Guide

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Discussion Overview

The discussion revolves around finding the vertex of the quadratic function f(x) = x^2 + 4x + 1. Participants explore methods to determine the x-coordinate of the vertex, including completing the square and using calculus. The scope includes mathematical reasoning and technical explanation.

Discussion Character

  • Mathematical reasoning
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant suggests that finding the vertex is related to completing the square and mentions that the standard form will reveal the vertex coordinates.
  • Another participant challenges the need for prior work to validate the correctness of the approach, emphasizing the importance of showing steps taken.
  • A later reply demonstrates the completion of the square method, providing the vertex coordinates as (-2, -3) and confirming the x-coordinate h = -2 through both completing the square and calculus methods.
  • There is uncertainty expressed by one participant regarding the correctness of the final answer provided.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the final answer, as one participant expresses doubt about the correctness of the solution presented.

Contextual Notes

The discussion includes various methods for finding the vertex, but there are no explicit resolutions to the correctness of the approaches or answers provided. Some assumptions about prior knowledge and methods are implied but not detailed.

poohbear1986
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Consider the function f(x)=x^2+4x+1

a)Find h, the x-coordinate of the vertex of this parabola.
 
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poohbear1986 said:
Consider the function f(x)=x^2+4x+1

a)Find h, the x-coordinate of the vertex of this parabola.

This must be related to Completing the Square. Your new version of the function (standard form) will contain information for the translated (moved away from standard position) graph, based on (h, k); you read this point directly from the function in standard form. Your book explains Completing the Square; are you using no intermediate algebra or no "elementary functions" book?
 
How can you possibly "make sure you are doing this right" when you haven't done anything? Show us what you have done and then we can tell you whether you are doing it right or not.
 
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f(x) = x^2 + 4x + 1
= x^2 + 4x + (2)^2 - (2)^2 + 1
= (x + 2)^2 - 3

coordinates of the turning point (-2, -3), hence the x-coordinate, h = -2

OR

f(x) = x^2 + 4x + 1

f '(x) = 2x + 4

at the turning point f '(x) = 0

2x + 4 = 0

2x = -4

x = -2

therefore, h the x-coordinate of the vertex of this parabola equals to -2

Hope my answer is correct...
 

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