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Warm-up!!

Warm-up!!. CCGPS Geometry Day 60 (11-5-13). UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12 ..A.REI.7, G.GPE.1,2 and 4 Today’s Question: How do we graph a parabola from a given equation in standard form? Standard: MCC9-12..G.GPE.2. Parabolas.

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Warm-up!!

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  1. Warm-up!!

  2. CCGPS GeometryDay 60 (11-5-13) UNIT QUESTION: How are the equations of circles and parabolas derived? Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4 Today’s Question: How do we graph a parabola from a given equation in standard form? Standard: MCC9-12..G.GPE.2

  3. Parabolas

  4. Parabolas Parabola: the set of points in a plane that are the same distance from a given point called the focus and a given line called the directrix. The cross section of a headlight is an example of a parabola... The light source is the Focus Directrix

  5. Here are some other applications of the parabola...

  6. d2 d1 Focus d2 d3 d1 d3 Vertex Directrix Notice that the vertex is located at the midpoint between the focus and the directrix... Also, notice that the distance from the focus to any point on the parabola is equal to the distance from that point to the directrix... We can determine the coordinates of the focus, and the equation of the directrix, given the equation of the parabola....

  7. (0, p) y = –p (If the x term is squared, the parabola is up or down) Standard Equation of a Parabola:(Vertex at the origin) Equation Focus Directrix y2 = 4px (p, 0) x = –p Equation Focus Directrix x2 = 4py (If the y term is squared, the parabola is left or right)

  8. Tell whether the parabola opens up down, left, or right. down right left

  9. Find the focus and equation of the directrix. Then sketch the graph. Opens right

  10. Find the focus and equation of the directrix. Then sketch the graph. Opens up

  11. Find the focus and equation of the directrix. Then sketch the graph. Opens down

  12. Find the focus and equation of the directrix. Then sketch the graph. Opens left

  13. Example 5: Determine the focus and directrix of the parabola (y – 2)2 = -16 (x - 5) : Direction: Vertex: Focus: Directrix:

  14. Example 6: Determine the focus and directrix of the parabola (x – 6)2= 8(y + 3) : Direction: Vertex: Focus: Directrix:

  15. 7. Write the equation in standard form by completing the square. State the VERTEX.

  16. You TRY!! 8. Write the equation in standard form by completing the square. State the VERTEX.

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