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Today in Precalculus

Today in Precalculus. Go over homework Notes: Parabolas with vertex other than (0,0) Homework. When a parabola with vertex (0,0) is translated horizontally h units and vertically k units the vertex becomes (h, k)

travis-albert
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Today in Precalculus

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  1. Today in Precalculus • Go over homework • Notes: Parabolas with vertex other than (0,0) • Homework

  2. When a parabola with vertex (0,0) is translated horizontally h units and vertically k units the vertex becomes (h, k) The translation does NOT change the focal length, the focal width, or the direction the parabola opens.

  3. Parabolas with vertex (h,k)

  4. Graphing a parabola by hand Let the focus F of a parabola be (2, -3) and its directrix be y = 4. Sketch and label the focus and directrix of the parabola. directrix F

  5. Graphing a parabola by hand Locate, sketch, and label the axis of the parabola What is its equation? x=2 Label and plot the vertex V of the parabola. Label it by name and coordinates. directrix V(2,0.5) F axis

  6. Graphing a parabola by hand What are the focal length and width of the parabola? focal length = p = -3.5 focal width =|4(-3.5)|=14 directrix V(2,0.5) F axis

  7. Use the focal width to locate, plot, and label the endpoints of a chord of the parabola that parallels the directrix. Sketch the parabola. Which direction does it open? downward What is its equation in standard form? (x – 2)2 = 4(-3.5)(y – .5) (x – 2)2 = -14(y – .5) directrix V(2,0.5) (-5,-3) F (9,-3) axis

  8. Graphing a parabola with the calculator (x – 2)2 = -14(y – .5) Solve for y (x – 2)2 = -14y + 7 (x – 2)2 – 7 = -14y

  9. Graphing a parabola with the calculator (y – 3)2 = 6(x – 4) Solve for y

  10. Homework Page 641: 3,4,22-44even

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