Grade 12 Unit 8
Grade 12 Unit 8
MATHEMATICS 1208 QUADRATIC EQUATIONS CONTENTS
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759 © MM by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc.
All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
ii
QUADRATIC EQUATIONS
OBJECTIVES Read these objectives. The objectives tell you what you should be able to do when you have successfully completed this LIFEPAC®. When you have completed this LIFEPAC, you should be able to: 1.
Identify the conic sections, find specific information relating to each of them, and graph related equations.
2.
Rotate and translate an equation into a simpler equation and sketch its curve.
1
___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________
I. CONIC SECTIONS: CIRCLE AND ELLIPSE
OBJECTIVE 1. Identify the conic sections, find specific information relating to each of them, and graph related equations.
2
THE CIRCLE
3
y
k(4,3) x
4
5
6
y
x
7
y
x
8
y
x
_________________
_________________
_________________
_________________ y
x
_________________
_________________
_________________
_________________ y
x
_________________
_________________
_________________
_________________
9
y
x
__________________
__________________
__________________
__________________ y
x
__________________
__________________
__________________
__________________ y
x
__________________
__________________
__________________
__________________
10
y
x
_____________________
______________________
_____________________
______________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
EQUATION FROM THREE POINTS
11
12
APPLICATIONS
13
14
15
THE ELLIPSE
16
17
18
__________________ _____,
y
_____, c = ______ __________________ x
__________________ __________________ __________________
19
____________________ ____________________
_____________________ y ___
___
_________
_____________________ _____________________ x _____________________ _____________________ _____________________ _____________________
_____________________ y ___
___
_________
_____________________ _____________________
x
_____________________ _____________________ _____________________ _____________________
____________________ y ___
___
_________
____________________ ____________________ ____________________
20
x
____________________ ____________________ ____________________
____________________ ___
___
y
___
____________________ x
____________________ ____________________ ____________________ ____________________ ____________________
y ____________________ ____________________ ___
___
___
x
____________________ ____________________
21
_______________________ _______________________ _______________________ _______________________
_______________________ y _______________________ ___
___
____
_______________________
x
_______________________ _______________________ _______________________ _______________________ _______________________
_______________________
y
_______________________ ___
___
___
_______________________ _______________________ _______________________ _______________________ _______________________ _______________________
22
x
23
24
_______________________
y
_______________________ ___
___
____
_______________________
x
_______________________ _______________________ _______________________ _______________________ _______________________
_______________________
y
_______________________ ___
___
____
_______________________ _______________________ _______________________ _______________________ _______________________ _______________________
25
x
_______________________ y _______________________ ___
___
____
_______________________
x
_______________________ _______________________ _______________________ _______________________ _______________________
_______________________
y
_______________________ ___
___
____
_______________________ _______________________ _______________________ _______________________ _______________________ _______________________
26
x
APPLICATIONS
27
28
29
Review the material in this section in preparation for the Self Test. The Self Test will check your mastery of this particular section. The items missed on this Self Test will indicate specific areas where restudy is needed for mastery.
SELF TEST 1
30
31
y
x
y
x
y
x
Score Teacher Check
75 94 32
_______________________ _______________________ Initial Date
MATHEMATICS 1208 QUADRATIC EQUATIONS CONTENTS
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759 © MM by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc.
All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
ii
QUADRATIC EQUATIONS
OBJECTIVES Read these objectives. The objectives tell you what you should be able to do when you have successfully completed this LIFEPAC®. When you have completed this LIFEPAC, you should be able to: 1.
Identify the conic sections, find specific information relating to each of them, and graph related equations.
2.
Rotate and translate an equation into a simpler equation and sketch its curve.
1
___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________ ___________________________________________________________________________________________________
I. CONIC SECTIONS: CIRCLE AND ELLIPSE
OBJECTIVE 1. Identify the conic sections, find specific information relating to each of them, and graph related equations.
2
THE CIRCLE
3
y
k(4,3) x
4
5
6
y
x
7
y
x
8
y
x
_________________
_________________
_________________
_________________ y
x
_________________
_________________
_________________
_________________ y
x
_________________
_________________
_________________
_________________
9
y
x
__________________
__________________
__________________
__________________ y
x
__________________
__________________
__________________
__________________ y
x
__________________
__________________
__________________
__________________
10
y
x
_____________________
______________________
_____________________
______________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
_________________________________
EQUATION FROM THREE POINTS
11
12
APPLICATIONS
13
14
15
THE ELLIPSE
16
17
18
__________________ _____,
y
_____, c = ______ __________________ x
__________________ __________________ __________________
19
____________________ ____________________
_____________________ y ___
___
_________
_____________________ _____________________ x _____________________ _____________________ _____________________ _____________________
_____________________ y ___
___
_________
_____________________ _____________________
x
_____________________ _____________________ _____________________ _____________________
____________________ y ___
___
_________
____________________ ____________________ ____________________
20
x
____________________ ____________________ ____________________
____________________ ___
___
y
___
____________________ x
____________________ ____________________ ____________________ ____________________ ____________________
y ____________________ ____________________ ___
___
___
x
____________________ ____________________
21
_______________________ _______________________ _______________________ _______________________
_______________________ y _______________________ ___
___
____
_______________________
x
_______________________ _______________________ _______________________ _______________________ _______________________
_______________________
y
_______________________ ___
___
___
_______________________ _______________________ _______________________ _______________________ _______________________ _______________________
22
x
23
24
_______________________
y
_______________________ ___
___
____
_______________________
x
_______________________ _______________________ _______________________ _______________________ _______________________
_______________________
y
_______________________ ___
___
____
_______________________ _______________________ _______________________ _______________________ _______________________ _______________________
25
x
_______________________ y _______________________ ___
___
____
_______________________
x
_______________________ _______________________ _______________________ _______________________ _______________________
_______________________
y
_______________________ ___
___
____
_______________________ _______________________ _______________________ _______________________ _______________________ _______________________
26
x
APPLICATIONS
27
28
29
Review the material in this section in preparation for the Self Test. The Self Test will check your mastery of this particular section. The items missed on this Self Test will indicate specific areas where restudy is needed for mastery.
SELF TEST 1
30
31
y
x
y
x
y
x
Score Teacher Check
75 94 32
_______________________ _______________________ Initial Date
