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? 

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