Axis of Symmetry of y=a(x-r_1)(x+r_2)

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Homework Help Overview

The discussion revolves around the equation of a parabola given in the form y=a(x-r_1)(x+r_2) and focuses on determining the axis of symmetry and the vertex of the parabola.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the coefficients of the quadratic form and the axis of symmetry, questioning how to derive the vertex's x-coordinate from the given equation.

Discussion Status

There is ongoing exploration of the concepts related to the axis of symmetry and vertex of the parabola. Multiple participants are raising similar questions about the derivation process, indicating a shared uncertainty in understanding the relationship between the parameters of the equation and the geometric properties of the parabola.

Contextual Notes

Some participants express confusion regarding the application of the standard formula for the axis of symmetry and how it relates to the specific coefficients in the context of the given equation.

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Problem 1.
Consider the equation y=a(x-r_1)(x+r_2)
Write the equation of the axis of symmetry.
 
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That is just a simple parabola:
[tex]y = ax^2 - ax(r_1 - r_2) - ar_1r_2[/tex]
Where is the 'vertex' of this parabola? What is its X coordinate?
 
How do you get the axis of symmetry..vertex..etc...

How would you get the axis of symmetry: x=-b/2a from b=-ax(r_1-r_2) and a= 1 or just a?
 
How do you get the axis of symmetry..vertex..etc...

How would you get the axis of symmetry: x=-b/2a from b=-ax(r_1-r_2) and a= 1 or just a?
 
How do you get the axis of symmetry..vertex..etc...

How would you get the axis of symmetry: x=-b/2a from b=-ax(r_1-r_2) and a= 1 or just a?
 
How do you get the axis of symmetry..vertex..etc...

How would you get the axis of symmetry: x=-b/2a from b=-ax(r_1-r_2) and a= 1 or just a?
 

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