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Some Basic Algebraic Functions: Quadratic Functions

Explore Quadratic functions

A Quadratic function comes with the standard form of y = ax2 + bx + c, when the highest power over the x variable(s) is 2.

Please note that when "a" is positive, the parabola opens upward, and the vertex is the minimum value of the function. On the other hand, if "a" is negative, the graph opens downward, and the vertex is the maximum value of the function.




Below, explore the interactive graph that allows you to change the a, b, and c values in a quadratic equation and view how the resulting parabola changes.  Please note that the initial quadratic function shown in the graph is y = x2 (refresh the graph to return to y = x2).

  • How does  the parabola behave when "a" becomes positive?
  • How does the parabola behave when "a" becomes negative?
  • How does the parabola behave when "a" approaches 0 ?
  • What happens if "a=0"?
  • Describe how the parabola moves when
    1.  b = 0,
    2. b > 0  
    3. b < 0
  • Describe how the parabola moves when
    1.  c = 0, 
    2. c > 0  
    3. c < 0




Created by peer tutors under the direction of Learning Centre faculty at Douglas College, British Columbia.


Project Coordinator and LibGuide developer

 Mina Sedaghatjou










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