Pre-Calculus I 9.3 The Parabola Definition of a Parabola ...

Pre-Calculus I
9.3 – The Parabola
Definition of a Parabola

Example – Find the vertex and the axis of symmetry of the parabola given
by y  2(x  3)2  4. Does it open up or down?

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Standard Form of the Equation of a Parabola

Example – Find the focus and the directrix of the parabola given

by y2  24x.

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Using the Standard Form of the Equation of a Parabola

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Example – Find the focus and the directrix of the parabola

given by x2  4 y.

Example – Find the focus and the directrix of the parabola

given by y2  12x.

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Translations of Parabola

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Example – Find the vertex, focus and directrix of the parabola

given by (x-3)2  8( y 1).

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Example – Find the vertex, axis, focus, and directrix of the parabola
by completing the square on the equation

8y=2x2 12x 14.

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Applications
Applications of Parabolas- cables on suspension bridges, arches
on bridges, solar cookers, reflectors on lights, satellite dishes

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A student scientist wants to construct a solar cooker which is

Example – in the shape of a parabolic dish with a diameter of 6 feet and a

depth of 1 foot. Where should the cooker (focus) be located

to get the maximum reflected sun rays to cook the food.

6 feet (3,1)
cook 1 foot
er

(0,0)

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