 # 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.

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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 Parabolas

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. Directrix The light source is the Focus The cross section of a headlight is an example of a parabola...

Here are some other applications of the parabola...

Directrix Focus d1d1 d1d1 d2d2 d2d2 d3d3 d3d3 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.... Vertex Notice that the vertex is located at the midpoint between the focus and the directrix...

Standard Equation of a Parabola: (Vertex at the origin) EquationFocusDirectrix x 2 = 4py (0, p)y = –p EquationFocusDirectrix y 2 = 4px (p, 0)x = –p (If the x term is squared, the parabola is up or down) (If the y term is squared, the parabola is left or right)

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

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

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

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

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

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

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

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

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

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