Student Practice: 11.3 The Parabola
Practice:Find the focus and directrix of the parabola with the given equation, then graph.y2=16xy2=4xy2=-8xy2=-12xx2=-16yx2=8yx2=-16yx2=-20yy2-6x=0x2-6y=08x2+4y=08y2+4x=0Find the standard form of the equation of each parabola satisfying the given conditions.Focus 7,0; Directrix x=-7Focus 9,0; Directrix x=-9Focus -5,0; Directrix x=5Focus -10,0; Directrix x=10Focus 0,15; Directrix y=-15Focus 0,20; Directrix y=-20Focus 0,-25; Directrix y=25Focus 0,-15; Directrix y=15Parabola Application ProblemsA satellite dish, like the one below, is the shape of a parabolic surface. Signals coming from a satellite strike the surface of the dish and are reflected to the focus, where the receiver is located. The satellite dish shown has a diameter of 12 feet and a depth of 2 feet. How far from the base of the dish should the receiver be placed?The towers of the Golden Gate Bridge connecting San Francisco to Marin Counter are 1280 meters apart and rise 160 meters above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 200 meters from a tower? Round to the nearest meter.The towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 100 feet from a tower?The parabolic arch shown in the figure is 50 feet above the water at the center and 200 feet wide at the base. Will a boat that is 30 feet tall clear the arch 30 feet from the center?Challenge Plus:Use the vertex and the direction in which the parabola opens to determine the relation’s domain and range. Is the relation a function?y2+6y-x+5=0y=-x2+4x-3x=-4(y-1)2+3y2-2y-x-5=0y=-x2-4x+4x=-3(y-1)2-2Practice:Focus: 4,0; Directrix: x=-4Focus: 1,0; Directrix: x=-1Focus: -2,0; Directrix: x=2Focus: -3,0; Directrix: x=3Focus: 0,4; Directrix: y=-4Focus: 0,2; Directrix: y=-2Focus: 0,-4; Directrix: y=4Focus: 0,-5; Directrix: y=5Focus: 32,0; Directrix: x=-32Focus: 0,32; Directrix: y=-32Focus: 0,-18; Directrix: y=18Focus: -18,0; Directrix: x=18y2=28xy2=36xy2=-20xy2=-40xx2=60yx2=80yx2=-100yx2=-60yThe receiver should be located 4.5 feet from the base of the dishThe height is 76 metersThe height is 90 feetYes, the boat will clear the arch. The height of the bridge is 45.5 feet.Challenge Plus: The vertex is (-4, 3)Opens to the rightDomain: [-4,∞)Range: -∞,∞The relation is not a functionThe vertex is (-6, 1)Opens to the rightDomain: [-6,∞)Range: -∞,∞The relation is not a functionThe vertex is (2, 1)Opens downwardDomain: -∞,∞Range: (-∞,1]The relation is a functionThe vertex is (-2, 8)Opens downwardDomain: -∞,∞Range: (-∞,8]The relation is a functionThe vertex is (3, 1)Opens leftDomain: (-∞,3]Range: -∞,∞The relation is not a functionThe vertex is (-2, 1)Opens to the leftDomain: (-∞,-2]Range: -∞,∞The relation is not a function ................
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