11.1 Parabolas Name: 1
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1 Algebra 2 Write your questions and thoughts here! 11.1 Parabolas Name: 1 Distance Formula The distance between two points, and, is Midpoint Formula The midpoint between two points, and, is,, RECALL: Standard form of a quadratic function: Vertex form of a quadratic function: The graph is called a. What s old: The graph opens up or down What s new: Solve for LABEL THE GRAPH: vertex axis of symmetry focus directrix Transformational Form Opens up or down with a vertex at,. Opens left or right with a vertex at,. What is? What is the distance between the focus and the directrix?
2 Write your questions and thoughts here! 11.1 Parabolas 2 For each equation, identify all of the parts listed, then sketch a graph Coordinate of vertex: Focal Width: The of the parabola at the. The width is Coordinate of vertex: 3. If 1, 4 is the vertex and 5, 4 is the focus, write an equation for the parabola. 4. If 3, 6 is the focus and 1 is the directrix, write an equation for the parabola. Algebra Skillz: 1. Graph 31 Multiply Sketch a graph of the given information. 2. Write out the shell of the equation. 4 identify if 4p is positive or negative. 3. What is squared, or? 4. Find the vertex. Plug into the equation. 5. Find. 6. Write out your final equation. Double check if 4 is positive or negative. Solve by factoring
3 11.1 Practice Parabolas Name: In exercises 1 4, Sketch the graph of the given equation and fill in the blanks for the given information Coordinate of vertex: Coordinate of vertex: Coordinate of vertex: Coordinate of vertex:
4 In exercises 5 14, find an equation for the parabola that satisfies the given condition. Use transformational form (just like the notes, the quantity squared will be isolated). 5. Vertex: 0, 0, focus: 3, 0 6. Vertex: 4, 4, focus: 2, 4 7. Vertex: 5, 6, focus: 5, 3 8. Vertex: 4, 3, directrix: 6 9. Vertex: 1, 5, directrix: Vertex: 2, 8, directrix: Focus: 0, 1, directrix: Focus: 3, 4, directrix: Focus: 4, 9, directrix: Focus: 8,, directrix: 1. Sketch a graph of the given information. 2. Write out the shell of the equation. 4 identify if 4p is positive or negative. 3. What is squared, or? 4. Find the vertex. Plug into the equation. 5. Find. 6. Write out your final equation. Double check if 4 is positive or negative.
5 11.1 Application and Extension Find an equation for the parabola that satisfies the given condition. Use transformational form. 1. Vertex: 4, 3, Focus: 4, 0 2. Focus: 8, 7, directrix: 5 3. In order to watch the Armed Forces Network, you need an AFN decoder along with a satellite. In order to better understand conics, Mr. Kelly climbed on your roof and took down your satellite dish creeper! Laying it on the ground pointing straight up, the receiver is located at the focus, which is 14 inches above the vertex. The satellite is 50 inches wide (think about the value). a. Draw a sketch of the satellite fitting the above information. b. Find an equation for the cross section of the dish assuming the vertex is at the origin. c. How deep is the dish? 4. While camping in Switzerland, you discover the campground will not allow you to make any fires. The problem is you brought hotdogs to eat for lunch every day of the trip! To solve the problem, you decide to build a solar hot dog cooker. You take a large piece of cardboard and build a parabolic trough that is 12 inches wide and 4 inches deep. Next, you line the trough with tin foil to reflect the heat of the sun. You then create a hole in the sides at the focus of each parabola. Your hot dog is then placed on a skewer through the focus so that the sun is reflecting and cooking your meal. How far from the bottom should the wire be placed? SAT Prep: 1. What is the focus of the graph shown? (A) 0, 3 (B) 0, 3 (C) 3, 0 (D) 3, 0 2. The distance between 3, 1 and 3, is What is a positive value for?
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