# 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 $x\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}p\hspace{0.17em}.\hspace{0.17em}$ With ...

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