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Lets study Parabolas by exploring the focus and directrix

Notes:PARABOLAS. Lets study Parabolas by exploring the focus and directrix.

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Lets study Parabolas by exploring the focus and directrix

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  1. Notes:PARABOLAS Lets study Parabolas by exploring the focus and directrix There is a chart on page 171 of the Pearson textbook where you can copy formulas and memorize. I plan to show you how to do these problems with just memorizing the vertex form of parabolas. Copy chart below if you wish to see both.

  2. Notes: Parabola, Focus, DIrectrix A parabola is the set of all points in a plane that are the same distance from a fixed line and a fixed point not on the line. The fixed point is called the FOCUS. The fixed line is called the DIRECTRIX.

  3. To be a parabola……The two red line segments must be the same length!! Focus Is the point (0,3) Directrix Note that the distance from the vertex to the focus point is the same as the distance as the vertex to the directrix… This distance is the “c” value.

  4. Vertex form : with a slight new look since we are studying the focus and directrix Previous Form using “a” (vertical stretch) New Form using “c” (focus point) Opens UP if Opens DOWN if Notice:

  5. Vertex form : How about parabolas that open sideways vs. up and down Previous Form using “a” (vertical stretch) New Form using “c” (focus point) Opens Right if Opens LEFT if Notice:

  6. Write an equation for this parabola! Vertex is: or Focus point is at : Directrix is at: We could write the equation for this if we knew the value of “c” Opens up so F c = distance from vertex to Focus and directrix!!! X goes with h and y goes with k

  7. Now you will graph parabolas Latus Rectum: move 2c out from the focus to get 2 more points on the parabola Extra hint to help get 2 easy points on the graph of parabolas This will make more sense when we apply it to the next example.

  8. Graph the PARABOLA Vertex Form: Parabola opens: right (-3,2) Axis of Symmetry: y = 2 vertex : Find the focus and directrix : X = -5 4 Latus Rectum = 2c =

  9. Convert the equation to a parabola in vertex form Find the: vertex: focus: directrix: Complete the square (7,2) • x= a(y-k)2 + h

  10. Find the vertex, focus and directrix: Find the: vertex: focus: directrix: Complete the square or Try this: (2,-2)

  11. Find the equation of a parabola with a focus (2,-3) and a directrix of x = -4 (the book shows this a different way p.174) Sketch to find the direction the parabola opens, the c value, and the vertex. Find a, h, and k to get vertex form Find the: direction: vertex: c value: Opens right

  12. HW: Parabolas Due next class!

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