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

[Loppyfoot]

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!

 

[Mark44]

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.

 

[Loppyfoot]

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

 

[Mark44]

You skipped a step - you need to find the equation of the tangent line first.

 

[Loppyfoot]

so the equation of the tangent line is y=-2x-3.


How would I translate the y=mx+b into the parametric form?

 

[Mark44]

Let x = t. Then you have y = -2t - 3, x = t.