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Unformatted text preview: is to determine the equation of the parabola suggested to us by this data. For simplicity, we’ll assume the vertex is (0, 0) and the parabola opens upwards. Our standard form for such a parabola is x2 = 4py . Since the focus is 2 units above the vertex, we know p = 2, so we have x2 = 8y . Visually, 414 Hooked on Conics y (6, y ) 12 units wide ? 2 −6 6 x Since the parabola is 12 feet wide, we know the edge is 6 feet from the vertex. To find the depth, we are looking for the y value when x = 6. Substituting x = 6 into the equation of the parabola yields 62 = 8y or y = 36/8 = 9/2 = 4.5. Hence, the dish will be 9/2 or 4.5 feet deep. 7.3 Parabolas 7.3.1 415 Exercises 1. Sketch the graph of the given parabola. Find the vertex, focus and directrix. Include the endpoints of the latus rectum in your sketch. (a) (y − 2)2 = −12(x + 3) (b) (y + 4)2 = 4x (c) (x − 3)2 = −16y (d) x + 72 3 =2 y+ 5 2 (e) (x − 1)2 = 4(y + 3) (f) (x + 2)2 = −20(y − 5) (g) (y − 4)2 = 18(x − 2) (h) y + 32 2 = −7...
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