5.1 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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5.1 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 The Parabola always wraps around the focus directrix vertex p “p” is The distance between the focus and the vertex or the vertex and the directrix

Opens Up or Down Opens Left or Right V (h, k) V (h, k) F (h, k + p) x p p p x p 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.

Homework 5.1 Worksheet