Algebra II Section 8-2 Parabolas (the dreaded lesson)

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Presentation transcript:

Algebra II Section 8-2 Parabolas (the dreaded lesson)

Conic Sections

Find a point equidistant from (2, 3) and the line y = -1 Distance from (x, y) to (2, 3)=Distance from (x, y) to (x, -1) This is a parabola!

Properties of Parabolas All incoming parallel rays are reflected to the same point (focus). This is true for light, sound, radio, …

Vertex = (h, k) Focus Line segment through the focus Parallel to the directrix Name : Latus Rectum. a ky Directrix 4 1 

Sideways? See chart on page 422 Mythbusters Illusion

Parabola A Parabola B Focus of A Focus of B

Find the Focus, Vertex, Directrix, Axis of Sym., Length of the L.R. y = -2x 2 – 20x + 9 Put in Vertex Form y = -2(x + 5) Focus = (-5, ) Vertex = (-5, 59) Directrix y = Length of L.R. = 0.5 Axis of Sym. x = -5

Page 423 # 1-41 odd