Graphing ParabolasA series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.
Introduction to Parabolas When graphing a quadratic equation, the resulting shape is not a straight line, but instead a shape called a parabola. Parabolas vary in direction and shape. The lowest or highest point in a parabola is called a vertex, which lies on the axis of symmetry. If the leading coefficient of the term to the second degree is positive, the parabola faces up. If it is negative, the parabola faces down.
Finding the Vertex of a Parabola by Completing the Square In order to graph a parabola, we need to find several pieces of information, including the vertex. One way to find the vertex of a parabola is to turn the standard form of the quadratic equation into vertex form by completing the square. The primary difference between solving a quadratic by completing the square and putting an equation into vertex form is substituting a "y" for the "0" in the initial equation.
Finding Intercepts, Domain, Range and Vertex of a Parabola When graphing and describing the characteristics of a parabola, it is important to know several key pieces of information. The parabola intercepts describe where the parabola intersects the x-axis and the y-axis while the vertex of a parabola is the highest (or lowest) point of the parabola. Knowing the domain and range of a parabola is also helpful when graphing.
Finding the Maximum or Minimum of a Quadratic Quadratic graphs have several properties such as shape, vertex and direction that help us solve several types of application questions. The vertex, the quadratic minimum and the quadratic maximum are also helpful when answering problems associated with area, speed and direction. We find the minimum if the parabola opens "up" and the maximum if the parabola opens "down."
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