Advanced Algebra /Pre-Calculus Name:______
Warm-Up Date ______Block _____
- Graph the parabola make sure to label the vertex, focus, directrix and axis of symmetry:
Vertex:
Axis of symmetry:
a =
Focus:
Directrix:
Endpoints of Latus Rectum:
- Put the following equations in Standard Form.
a) b)
Advanced Algebra /Pre-Calculus Name:______
9.2 The Parabola (Part 2) NOTES Date ______Block _____
Objectives:
- Given parabola facts, write the equation and sketch a complete graph.
- Given a parabolic graph, write its equation using the vertex and a point on it.
- Apply parabola ideas to real-world problems.
Example 1:
The focus of a parabola is (0, 2) and the vertex is (0, 0).
Vertex:
Axis of symmetry:
a =
Focus:
Directrix:
Endpoints of Latus Rectum:
Equation:
Graph
Example 2:
The focus is (-4, 0) and the vertex is (0, 0).
Vertex:
Axis of symmetry:
a =
Focus:
Directrix:
Endpoints of Latus Rectum:
Equation:
Graph
Example 3:
The focus is (0, -1) and the directrix is y = 1.
Vertex:
Axis of symmetry:
a =
Focus:
Directrix:
Endpoints of Latus Rectum:
Equation:
Graph
Example 4:
The vertex is (0, 0) and the x-axis is the axis of symmetry.
The parabola contains the point (2, 3).
Vertex:
Axis of symmetry:
a =
Focus:
Directrix:
Endpoints of Latus Rectum:
Equation:
Graph
Example 5:
The vertex is at (4, -2) and the focus is at (6, -2).
Vertex:
Axis of symmetry:
a =
Focus:
Directrix:
Endpoints of Latus Rectum:
Equation:
Graph
Example 6:
Write an equation for each parabola below, given two points.
A.]______B.]______
Applications of all Conics
Example 7: Paraboloid of Revolution
A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at its opening and 4 feet deep at its center, at what position should the receiver be placed?
Example 8: Suspension Bridge
The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at a height of 10 feet midway between the towers, what is the height of the cable at a point 50 feet from the center of the bridge?
Example 9: The arch used to support a bridge is in the shape of half of an ellipse (a semi-ellipse). If the river is 30 meters wide, and the center of the arch is 9 meters high, Write an equation for the ellipse in which the x-axis coincides with the water level. What is the height of the arch (above the water) at distances of 10 and 20 meters from the center?
Example 10: A racetrack is in the shape of an ellipse 100 feet long and 50 feet wide. What is the width 10 feet from a vertex?
Example 11: Match the graphs with the equations:
Label the Vertex, Focus, and Directrix after finding the graph.
1)y2= -4x
2)(y-1)2=4(x-3)
3)x2=2y
4)(x+3)2=-2(y-1)
A) B)
C) D)