Finding the parametric form of a tangent line vectors

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SUMMARY

The discussion focuses on finding the parametric form of the tangent line to the graph of the function y=2x²−5x+3 at the point where x=2. The tangent line is determined to be y=3x−5. The participants clarify that the parametric form can be expressed as +t, where (x0,y0) and (x1,y1) can be any two points on the tangent line, emphasizing that multiple choices for these points are valid.

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives and tangent lines.
  • Familiarity with the quadratic function and its properties.
  • Knowledge of parametric equations and their representation.
  • Ability to evaluate functions at specific points.
NEXT STEPS
  • Study the concept of derivatives to understand how to find tangent lines.
  • Learn about parametric equations and their applications in geometry.
  • Explore the properties of quadratic functions and their graphs.
  • Practice finding tangent lines for various functions using different points.
USEFUL FOR

Students studying calculus, particularly those learning about derivatives and tangent lines, as well as educators seeking to clarify these concepts for their students.

Wm_Davies
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Homework Statement


Find the parametric form for the tangent line to the graph of y=2x2−5x+3 at x=2 is

Homework Equations


I have no clue!


The Attempt at a Solution


I found the tangent line to be y=3x-5

I know that the answer has to be in the form...

<x0,y0>+t<x1-x0,y1-y0>

I have absolutely no idea what is x0,y0,x1, or y1.

So I am just really confused on how to put it in the requested form.
 
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There are a lot of choices for x0, y0, x1 and y1. Pick any two points on your tangent line. Put x=2 and get y=1. So (2,1) is a choice for (x0,y0). Pick x=3. What do you get for y? That's a choice for (x1,y1). There's no one form for a parametric line. Pick any two points you want.
 
Thank you Dick. That actually makes a lot of sense! I was just making the problem too hard (as usual).
 

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