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Unit 6.2 Introduction to Conics Parabolas

 1. 

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin.

Horizontal axis and passes through the point mc001-1.jpg
a.
mc001-2.jpg mc001-3.jpg
b.
mc001-4.jpg mc001-5.jpgx
c.
mc001-6.jpg mc001-7.jpgx
d.
mc001-8.jpg mc001-9.jpgy
e.
mc001-10.jpg x
 

 2. 

Find the vertex, focus, and directrix of the parabola.

mc002-1.jpg
a.
Vertex: mc002-2.jpg; Focus: mc002-3.jpg; Directrix: mc002-4.jpg
b.
Vertex: mc002-5.jpg; Focus: mc002-6.jpg; Directrix: mc002-7.jpg
c.
Vertex: mc002-8.jpg; Focus: mc002-9.jpg; Directrix: mc002-10.jpg
d.
Vertex: mc002-11.jpg; Focus: mc002-12.jpg; Directrix: mc002-13.jpg
e.
Vertex: mc002-14.jpg; Focus: mc002-15.jpg; Directrix: mc002-16.jpg
 

 3. 

Find the vertex, focus, and directrix of the parabola.

mc003-1.jpg
a.
Vertex:mc003-2.jpg; Focus: mc003-3.jpg; Directrix: mc003-4.jpg
b.
Vertex:mc003-5.jpg; Focus: mc003-6.jpg; Directrix: mc003-7.jpg
c.
Vertex:mc003-8.jpg; Focus: mc003-9.jpg; Directrix: mc003-10.jpg
d.
Vertex:mc003-11.jpg; Focus: mc003-12.jpg; Directrix: mc003-13.jpg
e.
Vertex:mc003-14.jpg; Focus: mc003-15.jpg; Directrix: mc003-16.jpg
 

 4. 

Find the standard form of the equation of the parabola with the given characteristics.

Vertex: mc004-1.jpg; directrix: mc004-2.jpg
a.
mc004-3.jpg
b.
mc004-4.jpg
c.
mc004-5.jpg
d.
mc004-6.jpg
e.
mc004-7.jpg
 

 5. 

The equations of a parabola and a tangent line to the parabola are given. Select the correct graph of both equations in the same viewing window.

Parabola: mc005-1.jpg
Tangent Line: mc005-2.jpg
a.

mc005-3.jpg
d.

mc005-6.jpg
b.

mc005-4.jpg
e.

mc005-7.jpg
c.

mc005-5.jpg
 

 6. 

The equations of a parabola and a tangent line to the parabola are given. Select the correct graph of both equations in the same viewing window.

Parabola: mc006-1.jpg
Tangent Line: mc006-2.jpg 
a.

mc006-3.jpg
d.

mc006-6.jpg
b.

mc006-4.jpg
e.

mc006-7.jpg
c.

mc006-5.jpg
 

 7. 

The receiver in a parabolic satellite dish is 4.5 feet from the vertex and is located at the focus (see figure). Write an equation for a cross section of the reflector. (Assume that the dish is directed upward and the vertex is at the origin.)

mc007-1.jpg
mc007-2.jpg
a.
mc007-3.jpgor mc007-4.jpg
b.
mc007-5.jpg or mc007-6.jpg
c.
mc007-7.jpgor mc007-8.jpg
d.
mc007-9.jpg or mc007-10.jpg
e.
mc007-11.jpg or mc007-12.jpg
 

 8. 

Roads are often designed with parabolic surfaces to allow rain to drain off. A particular road that is 32 feet wide is 0.2 foot higher in the center than it is on the sides (see figure).
Find an equation of the parabola that models the road surface. (Assume that the origin is at the center of the road.)

mc008-1.jpg

where mc008-2.jpg ft, mc008-3.jpg
a.
mc008-4.jpg or mc008-5.jpg
b.
mc008-6.jpg or mc008-7.jpg
c.
mc008-8.jpg or mc008-9.jpg
d.
mc008-10.jpg or mc008-11.jpg
e.
mc008-12.jpg or mc008-13.jpg
 

 9. 

Find the vertex and directrix of the parabola.
mc009-1.jpg
a.
vertex: mc009-2.jpg          directrix: mc009-3.jpg
b.
vertex: mc009-4.jpg          directrix: mc009-5.jpg
c.
vertex: mc009-6.jpg          directrix: mc009-7.jpg
d.
vertex: mc009-8.jpg          directrix: mc009-9.jpg
e.
vertex: mc009-10.jpg          directrix: mc009-11.jpg
 

 10. 

Use a graphing utility to graph the parabola.

mc010-1.jpg

a.

mc010-2.jpg
d.

mc010-5.jpg
b.

mc010-3.jpg
e.

mc010-6.jpg
c.

mc010-4.jpg
 



 
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