Simulic
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Graphing quadratics – coefficients, vertex form, focus and directrix

MathematicsFunctions & GraphsAges 15–16

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Four screens: Explore (drag the a, b, c sliders and see each term ax², bx and c separately), Standard Form (integer coefficients set with buttons; toggle the vertex, axis of symmetry, roots and y-intercept), Vertex Form (drag the vertex directly to change h and k) and the extension Focus and Directrix (drag the focus and a point on the parabola to see that the two distances are always equal). Adapted from the "Graphing Quadratics" simulation by PhET Interactive Simulations, University of Colorado Boulder (CC BY 4.0); rewritten.

Lesson: Quadratic functions and their graphs

How to use

Parameters you can change

  • Starting screen Explore, Standard form, Vertex form, Focus and directrix
  • Explore: coefficient a -4–4
  • Explore: coefficient b -8–8
  • Explore: coefficient c -8–8
  • Explore: show each term separately
  • Standard form: coefficient a (integer, non-zero) -6–6
  • Standard form: coefficient b (integer) -10–10
  • Standard form: coefficient c (integer) -10–10
  • Standard form: show vertex
  • Standard form: show axis of symmetry
  • Standard form: show roots
  • Standard form: show y-intercept
  • Vertex form: coefficient a (non-zero) -4–4
  • Vertex form: vertex x-coordinate h -6–6
  • Vertex form: vertex y-coordinate k -6–6
  • Focus: vertex x-coordinate h -4–4
  • Focus: vertex y-coordinate k -4–4
  • Focus: focal distance |p| 0.5–4
  • Focus: opens downward
  • Focus: x-coordinate of point P on the parabola -6–6

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