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Center/vertex: (h, k) AOS: x = h Orientation: Vertical if +p then up and –p is down

Center/vertex: (h, k) AOS: x = h Orientation: Vertical if +p then up and –p is down. Focus: point p distance from vertex Directrix: line p distance from vertex EOLR: points 2p distance from focus Focal Width: how wide parabola is at focus (4p). Center/vertex: (h, k) AOS: y = k

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Center/vertex: (h, k) AOS: x = h Orientation: Vertical if +p then up and –p is down

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  1. Center/vertex: (h, k) • AOS: x = h • Orientation: Vertical if +p then up and –p is down • Focus: point p distance from vertex • Directrix: line p distance from vertex • EOLR: points 2p distance from focus • Focal Width: how wide parabola is at focus (4p) • Center/vertex: (h, k) • AOS: y = k • Orientation: Horizontal if +p then right if –p then left EOLR AOS 2p p AOS p Focus Focus vertex 2p 2p EOLR EOLR 2p p vertex p EOLR

  2. Steps to graph • Decide orientation • Find center • Find p • Plot center • Count p spaces to find Focus and Dirextrix • Count 2p spaces to find EOLR • Connect EOLR and Center with curve Ex 2) Graph Ex 1) Graph Orientation: vertical opens up Center: (2, -1) P= (20/4) = 5 Orientation: horizontal opens left Center: (0, -2) P= (16/4) - 4 Parabola

  3. Ex 4) Write the equation given Focus: (0, 4) Directrix: x = 3 • Pre-AP • Steps to write equation • Find center • Find p • Substitute Ex 3) Write the equation given Focus: (0, 3) Directrix: y = -3 The center is in between the focus and directrix. If you graph, then you will see that it is at (1.5. 4) and p=1.5 To hug the focus it would have to open left. The center is in between the focus and directrix. If you graph, then you will see that it is at (0, 0) and p=3 To hug the focus it would have to open up.

  4. Change to Conic Form: Complete the Square • 1 variable squared • 2 variables squared y2 + x + 10y + 26 = 0 y2 + 10y + ___ = -x – 26 + ___ (10/2)=5 then 52 =25 y2 + 10y + 25 = -x – 26 + 25 (y+5)2 = -x – 1 (y+5)2 = -(x +1) x2 + y2 -2x - 4y – 4 = 0 (x2 -2x + ___) + (y2 - 4y + ____) = - 4 + ____ + ____ (-2/2)=-1 then (-1)2=1 AND (-4/2)=-2 then (-2)2=4 (x2 -2x + 1) + (y2 - 4y + 4) = - 4 + 1 + 4 (x-1)2 + (y-2)2 = 1 • GMA (Group, move, add blanks) • Fill in blanks • Factor and simplify • Pre-AP Only • Squared variable coefficient >1 9x2 + 4y2 - 54x - 8y – 59 = 0 9x2 - 54x + 4y2 - 8y = 59 9(x2 - 6x +__) + 4(y2 - 2y + __) = 59 + 9(__) + 4(__) (-6/2)2=9 and (-2/2)2=1 9(x2 - 6x +9) + 4(y2 - 2y + 1) = 59 + 9(9) + 4(1) 9(x – 3)2 + 4(y – 1)2 = 144 6x2 + 12x - y + 15 = 0 6x2 + 12x + __ = y – 15 + ___ 6(x2 + 2x + __) = y – 15 + 6(__) (2/2)=1 then 12=1 6(x2 + 2x + 1) = y – 15 + 6(1) 6(x+1)2 = y – 9 • GMA (Group, move, add blanks) • Factor out GCF and add to blank on other side • Fill in blanks • Factor and simplify

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