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10.2 Parabolas

10.2 Parabolas. By: L. Keali’i Alicea. Parabolas. We have seen parabolas before. Can anyone tell me where? That’s right! Quadratics! Quadratics can take the form: x 2 = 4py or y 2 = 4px . Parts of a parabola. Focus

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10.2 Parabolas

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  1. 10.2 Parabolas By: L. Keali’i Alicea

  2. Parabolas • We have seen parabolas before. Can anyone tell me where? • That’s right! Quadratics! • Quadratics can take the form: x2 = 4py or y2 = 4px

  3. Parts of a parabola • Focus A point that lies on the axis of symmetry that is equidistant from all the points on the parabola.

  4. Parts of a parabola • Directrix A line perpendicular to the axis of symmetry used in the definition of a parabola.

  5. Focus Lies on AOS Directrix

  6. x2=4py y2=4px 2 Different Kinds of Parabolas

  7. Standard equation of Parabola (vertex @ origin)

  8. x2=4py, p>0 Focus (0,p) Directrix y=-p

  9. x2=4py, p<0 Directrix y=-p Focus (0,p)

  10. y2=4px, p>0 Directrix x=-p Focus (p,0)

  11. y2=4px, p<0 Directrix x=-p Focus (p,0)

  12. Identify the focus and directrix of the parabolax = -1/6y2 • Since y is squared, AOS is horizontal • Isolate the y2→ y2 = -6x • Since 4p = -6 • p = -6/4 = -3/2 • Focus : (-3/2,0) Directrix : x=-p=3/2 • To draw: make a table of values & plot • p<0 so opens left so only choose neg values for x

  13. Your Turn! • Find the focus and directrix, then graph x = 3/4y2 • y2 so AOS is Horizontal • Isolate y2→ y2 = 4/3 x • 4p = 4/3 p = 1/3 • Focus (1/3,0) Directrix x=-p=-1/3

  14. Writing the equation of a parabola. • The graph shows V=(0,0) • Directrex y=-p=-2 • So substitute 2 for p

  15. x2 = 4py • x2 = 4(2)y • x2 = 8y • y = 1/8 x2 and check in your calculator

  16. Your turn! • Focus = (0,-3) • X2 = 4py • X2 = 4(-3)y • X2 = -12y • y=-1/12x2 to check

  17. Assignment10.2 A (1-3, 5-19odd)10.2 B (2-20 even, 21-22)

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