Parabolas
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Introduction

     In this section, you will learn how to graph parabolas. Here is a list of the sections within this webpage:



     The definition of a parabola is the set of all points that are equidistant to a focal point and a line called a directrix. Howver, it is best recognized by its classic u-shape.

     Parabolas either open up, down, right, or left. The graphic below will show you how a parabola looks in comparison to its equation.

Equations of a Parabola

     When the x-value is being squared, the parabola opens up when the p-value is positive and down when the p-value is negative.

     On the other hand, when the y-value is being squared, the parabola opens right when the p-value is positive and left when the p-value is negative.

     The h-value and the k-value represents the location of the vertex, V(h,k). Therefore, it is important to know the location of the vertex in order to determine the exact equation of a parabola. Conversely, when the equation of a parabola is known, the exact location of the vertex can be determined.

     Here is a video and a quiz that will help you understand and assess your understanding of parabolas.

      ideo: Parabolas: Directrix, Focus, Vertex
      ideo: Parabolas: Graphing
      ideo: Parabolas: Building Equations
      uiz: Parabolas
      uiz: Paraboloid Receiver

    Here are videos related to the lessons above.

      ideo: Parabolas: Directrix, Focus, Vertex
      ideo: Parabolas: Graphing
      ideo: Parabolas: Building Equations

    After reading the lessons, try our quizmasters. MATHguide has developed numerous testing and checking programs to solidify these skills:

      uiz: Parabolas
      uiz: Paraboloid Receiver

    Here are activities related to the lessons above.

      ctivity: Conics: Supplemental

    Here related lessons to view.

      esson: Circles
      esson: Ellipses
      esson: Hyperbolas
      esson: Conic Sections
      esson: Graphing Lines
      esson: The Point-Slope Formula
      esson: Graphing Linear Inequalities
      esson: Flight of a Projectile
      esson: Completing the Square