Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

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Presentation transcript:

Parabolas a set of points whose distance to a fixed point (focus) equals it’s distance to a fixed line (directrix) A Parabola is -

Vertex is always between the focus & the directrix p vertex directrix p Vertex always wraps around the focus and goes away from the directrix

Opens Up or Down V (h, k) F (h, k + p) Directrix y = k – p Axis of Symmetry x = h If p > 0 opens Up If p < 0 opens Down Opens Left or Right V (h, k) F (h + p, k) Directrix x = h – p Axis of Symmetry y = k If p > 0 opens Right If p < 0 opens Left

Example 1 Find the standard form equation for the parabola with a focus at (-3, 2) and a directrix at y = 4.

Example 2 Find the standard form equation for the parabola with a vertex at (0, 0) and a directrix at y = – 4.

Example 3 Find the standard form equation for the parabola with a focus at (-6, 4) and a directrix at x = 2.

Example 4 Find the standard form equation for the parabola with a focus at (6, 2) and a vertex at (3, 2).

Example 5 Find the vertex, focus & directrix for

Example 6 Find the vertex, focus & directrix for

Example 7 Graph the parabola and label the vertex, focus and directrix.

You try!! Graph the equation. Label the vertex, focus, and directrix.

What is it? C, E, H or P C H 38 P H E