![Page 1: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/1.jpg)
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![Page 3: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/3.jpg)
Allowed Formulas
![Page 4: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/4.jpg)
Conic Sections are curves that result from the
intersection of a cone and a plane.
![Page 5: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/5.jpg)
PARTS OF A PARABOLA
7.2 – The Parabola
![Page 6: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/6.jpg)
7.2 – The Parabola
Find the vertex, focus, and the directrix of the following parabola.
Graph the equation.
2 14 8 25y y x+ = −
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
![Page 7: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/7.jpg)
PARTS OF AN ELLIPSE
major axisminor axis
The major axis is in the direction of the longest part of the ellipse
7.3 – The Ellipse
center focifoci
The vertices are at the ends of the major axis
![Page 8: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/8.jpg)
7.3 – The Ellipse
Analyze the equation; that is, find the center, foci, and vertices of the
ellipse. Graph the equation.
( ) ( )2 2
1 41
25 9
x y− ++ =
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
![Page 9: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/9.jpg)
7.3 – The Ellipse
Find an equation for the ellipse described. Graph the equation.
Foci at (0,3) and (-4,3); vertex at (-6,3)
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
![Page 10: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/10.jpg)
7.3 – The EllipseFall 2008 Final Exam
![Page 11: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/11.jpg)
7.3 – The Ellipse
Analyze the equation. Find the center, foci,
vertices, and graph the equation.2 24 3 8 6 5x y x y+ + − =
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−1
1
2
3
4
5
6
7
8
9
x
y
−10
−9
−8
−7
−6
−5
−4
−3
−2
![Page 12: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/12.jpg)
PARTS OF A HYPERBOLA
co
nju
gate
axis
The black dashes lines are asymptotes for the graphs.
transverse axis
7.4 – The Hyperbola
centerfocifoci
co
nju
gate
axis
transverse axis
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7.4 – The Hyperbola
Find the equation of the hyperbola whose graph is given below.
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−3
−2
−1
1
2
3
4
5
6
7
8
9
x
y
−10
−9
−8
−7
−6
−5
−4
![Page 14: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/14.jpg)
7.4 – The Hyperbola
Analyze the equation; that is, find the center, foci, and vertices of the
hyperbola. Graph the equation and include the asymptotes on your
sketch.
( ) ( )2 2
2 31
16 4
x y+ −− =
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
x
y
−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
![Page 15: Review for Module 5 test - aliamawportfolio.weebly.comaliamawportfolio.weebly.com/uploads/4/9/3/4/... · 7.2 –The Parabola Find the vertex, focus, and the directrix of the following](https://reader036.vdocuments.us/reader036/viewer/2022062607/6055d42ac209144213179b46/html5/thumbnails/15.jpg)
7.4 – The HyperbolaFall 2008 Final Exam
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