PRECALCULUS PROBLEM SESSION #14- PRACTICE PROBLEMS
Parabolas
A) Find the vertex, focus, and directrix of the parabolas and sketch its graph.
1. ๐ฆ=1
2๐ฅ2 2. ๐ฆ2= โ6๐ฅ 3. ๐ฅ2+ 6๐ฆ= 0
4. (๐ฅ โ 1)2+ 8(๐ฆ+ 2) 5. (๐ฅ+ 5)+(๐ฆ โ 1)2= 0 6. ๏ฟฝ๐ฅ +3
2๏ฟฝ2= 4(๐ฆ โ 2)
7. ๏ฟฝ๐ฅ +1
2๏ฟฝ2= 4(๐ฆ โ 1) 8. ๐ฆ=1
4(๐ฅ2โ2๐ฅ+ 5) 9. ๐ฅ=1
4(๐ฆ2+ 2๐ฆ+33)
10. ๐ฆ2+ 6๐ฆ+ 8๐ฅ+25 = 0 11. ๐ฆ2โ4๐ฆ โ 4๐ฅ= 0
B) Find the standard form of the equation of the parabola with its vertex at the origin.
1. Focus: (0, โ3
2) 2. Focus: (โ2,0) 3. Directrix: ๐ฆ=โ1
4. Directrix: ๐ฅ= 2 5. Horizontal axis and passes through the point (4,6)
6. 7.
C) Find the standard form of the equation of the parabola.
1. Vertex: (5, 2); Focus: (3,2) 2. Vertex: (0,4); Directrix: ๐ฆ= 2
3. Focus: (2,2); Directrix: ๐ฅ=โ2 4. 5.
D) Word problem
1. Each cable of a suspension bridge is suspended (in the shape of a parabola) between two towers
that are 120 meters apart and whose tops are 20 meters about the roadway. The cables touch
the roadway midway between the towers.
a. Create a sketch of the bridge. Draw a rectangular coordinate system on the bridge with
the center of the bridge at the origin. Identify the coordinates of the known points.
b. Find an equation for the parabolic shape of each cable.
