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...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details