Lesson Plan: Solving Quadratic Equations Using Graphs Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to graph a quadratic function of the form 𝑓(𝑥) = 𝑎𝑥² + 𝑏𝑥 + 𝑐, in order to solve the equation 𝑓(𝑥) = 0.


Students will be able to

  • understand that, for a quadratic function of the form 𝑓(𝑥)=𝑎𝑥+𝑏𝑥+𝑐
    • the solutions to the equation 𝑓(𝑥)=0 occur where the graph intersects the 𝑥-axis,
  • find the solutions to the equation 𝑓(𝑥)=𝑎𝑥+𝑏𝑥+𝑐=0
    • when given the graph of 𝑓(𝑥),
    • when points of the form (𝑥,0) that lie on the graph are specified,
    • by plotting the graph of 𝑓(𝑥) over a specified interval.


Students should already be familiar with

  • drawing graphs from tables of values,
  • graphing quadratic functions,
  • the fact that the equation 𝑓(𝑥)=𝑎𝑥+𝑏𝑥+𝑐=0 may have one, two, or no solutions.


Students will not cover

  • graphs of linear functions,
  • graphs of cubic functions (or higher),
  • solving quadratic equations by factorization,
  • solving quadratic equations using the quadratic formula,
  • quadratic functions with fractional, decimal, or irrational coefficients.

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