21.4 The Parabola

  • Directrix • Focus • Axis • Vertex • Standard Form of Equation • Axis along x-axis • Axis along y-axis • Calculator Display

In Chapter 7, we showed that the graph of a quadratic function is a parabola. We now define the parabola more generally and find the general form of its equation.

A parabola is defined as the locus of a point P(x, y) that moves so that it is always equidistant from a given line (the directrix) and a given point (the focus). The line through the focus that is perpendicular to the directrix is the axis of the parabola. The point midway between the focus and directrix is the vertex.

Using the definition, we now find the equation of the parabola with the focus at (p, 0) and the directrix x =  − p .  With ...

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