What is the parametric form for the tangent line to y = 2x^(2)+2x-1 at x = -1?

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Homework Help Overview

The problem involves finding the parametric form for the tangent line to the function y = 2x² + 2x - 1 at the point where x = -1. Participants are exploring the necessary steps to derive this form, including determining the slope of the tangent line and identifying a point on the line.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to find the slope of the tangent line at x = -1 and identify the corresponding point on the curve. There is a mention of translating the line equation into parametric form, with some participants questioning the steps involved in this translation.

Discussion Status

The discussion is ongoing, with some participants providing guidance on finding the slope and point for the tangent line. There is an exploration of how to express the tangent line in parametric form, but no consensus has been reached on the final representation.

Contextual Notes

Participants are working within the constraints of deriving the tangent line's equation and converting it to parametric form, with some confusion about the necessary steps involved.

Loppyfoot
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Homework Statement



The parametric form for the tangent line to the graph of y = 2x^(2)+2x-1 at x = -1 is

Homework Equations





The Attempt at a Solution



I am confused about where to begin this problem. Any thoughts?

Thanks!
 
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Loppyfoot said:

Homework Statement



The parametric form for the tangent line to the graph of y = 2x^(2)+2x-1 at x = -1 is

Homework Equations





The Attempt at a Solution



I am confused about where to begin this problem. Any thoughts?

Thanks!
The first step would be to find the slope of the tangent line at the point (-1, f(-1)). Once you have the slope of the tangent line, and a point on the tangent line - (-1, f(-1)), you can find the equation of the tangent line.

The final step would be to write the equation of the tangent line in parametric form.
 
So the slope of the tangent line would be:

y'=4x+2...plug in x=-1.

slope of tangent line at x=-1 is y'=-2.

A point on the line would be (-1,-1).

How would I translate this data into parametric form
 
You skipped a step - you need to find the equation of the tangent line first.
 
so the equation of the tangent line is y=-2x-3.


How would I translate the y=mx+b into the parametric form?
 
Let x = t. Then you have y = -2t - 3, x = t.
 

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