Parabola Tangent

https://www.desmos.com/calculator/mtbq4rkk2f

Start with the parabola

and then move it so that its vertex is at (1, 1).

Then draw a line through the origin that is tangent to the new parabola.

The question is, what is the slope of the line and what is the point of intersection? 

Teacher Manual

Curriculum Expectations

  • Use of Mathematical Processes

  • Investigating the Basic Properties of Quadratic Relations

  • Relating the Graph of y = x^2 and its Transformations

  • Solving Quadratic Equations

  • Solving Problems Involving Quadratic Relations