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9.2 Parabola Hyperbola/Parabola Quiz: FRIDAY Concis Test: March 26

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Parabola A parabola is defined in terms of a fixed point, called the focus, and a fixed line, called the directrix. In a parabola, the distance from any point, P, on the parabola to the focus, F, is equal to the shortest distance from P to the directrix. That is, PF = PD for any point, P, on the parabola.

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Standard Equation of a Parabola Horizontal directrix p > 0: opens up p < 0: opens down You go up and down the value of p to get your focus and directrix Vertical directrix p > 0: opens right p < 0: opens left You go left and right the value of p to get your focus and directrix.

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Something to keep in mind The focus should always be “in” your curve. The directrix should always be “outside” of your curve.

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Example: Graph. Label the vertex, focus, and directrix.

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You Try: Graph. Label the vertex, focus, and directrix.

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Example: Write the standard equation of the parabola with its vertex at the origin and with the directrix y = 4. Sketch a graph if you need to.

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You Try: Write the standard equation of the parabola with its vertex at the origin and with the directrix x = -6. Next

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Horizontal Directrix F(0,p) y = -p Back

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Vertical Directrix F(p,0) x = -p Back

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9.2 Continued Hyperbola/Parabola Quiz: FRIDAY! Conics Test: March 26

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Standard Equation of a Translated Parabola Horizontal DirectrixVertical Directrix

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Example: Write the standard equation of the parabola with its focus at (-3,2) and with the directrix y = 4 Sketch a graph if you need to.

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You Try: Write the standard equation of the parabola with its focus at (-6,4) and with the directrix x = 2.

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Example: Graph the parabola y 2 – 8y + 8x + 8 = 0. Label the vertex, focus, and directrix.

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Graph:

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You Try: Graph the parabola x 2 – 6x + 6y + 18 = 0. Label the vertex, focus, and directrix.

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Graph:

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Practice Parabola WS THIS IS A LOT: PRACTICE!

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