CK-12-Pre-Calculus Concepts

8.9. Inverse Matrices http://www.ck12.org   1 2 3 1 0 1 0 2 − 1  ·   x y z  =   96 36 − 12   Solution: A·   x y z ...

http://www.ck12.org Chapter 8. Systems and Matrices A=   1 2 3 1 0 1 0 2 − 1  ,A−^1 =   − 113 43 13 61 −^1613 3 −^13 −^13 ...

8.9. Inverse Matrices http://www.ck12.org A·A−^1 =A·B A−^1 ·   96 36 − 12  =B·   96 36 − 12  =B·C You need to create mat ...

http://www.ck12.org Chapter 8. Systems and Matrices 7.   −1 3 − 4 4 2 1 1 2 5   8.   4 5 8 9 0 1 0 3 − 2   9.   0 7 − ...

8.10. Partial Fractions http://www.ck12.org 8.10 Partial Fractions Here you will apply what you know about systems and matrices ...

http://www.ck12.org Chapter 8. Systems and Matrices Notice the squared term, linear term and constant term form a system of thre ...

8.10. Partial Fractions http://www.ck12.org 5 =A+D − 3 =− 2 A+B− 3 D+E − 1 =A−B+C+ 3 D− 3 E 4 =−D+ 3 E − 1 =E This is a system o ...

http://www.ck12.org Chapter 8. Systems and Matrices 2 x+ 4 (x− 1 )(x+ 3 )= 1 x+ 1 + 1 x+ 3 Concept Problem Revisited To decompos ...

8.10. Partial Fractions http://www.ck12.org 5 x− 2 ( 2 x− 1 )( 3 x+ 4 )= A 2 x− 1 + B 3 x+ 4 5 x− 2 =A( 3 x+ 4 )+B( 2 x− 1 ) 5 ...

http://www.ck12.org Chapter 8. Systems and Matrices Confirm your answer to #1 by adding the partial fractions. Confirm your ans ...

8.11. References http://www.ck12.org 8.11 References Laura Guerin. CK-12 Foundation. CK-12 Foundation.. CCSA CK-12 Foundation.. ...

http://www.ck12.org Chapter 9. Conics CHAPTER 9 Conics Chapter Outline 9.1 General Form of a Conic 9.2 Parabolas Contents http:/ ...

9.1. General Form of a Conic http://www.ck12.org 9.1 General Form of a Conic Here you will see how each conic section is the int ...

http://www.ck12.org Chapter 9. Conics As you tilt the plane even further and the slope of the plane equals the slope of the cone ...

9.1. General Form of a Conic http://www.ck12.org Before you start manipulating the general form of a conic equation you should b ...

http://www.ck12.org Chapter 9. Conics sides of thex^2 square. Notice what is missing to make this shape a perfect square? A litt ...

9.1. General Form of a Conic http://www.ck12.org Solution: First write out the equation with space so that there is room for the ...

http://www.ck12.org Chapter 9. Conics f. Hyperbola 2. 6 y^2 − 36 y+ 4 6 (y^2 − 6 y+ )+ 4 6 (y^2 − 6 y+ 9 )+ 4 − 54 6 (y− 3 )^2 − ...

9.2. Parabolas http://www.ck12.org 9.2 Parabolas Here you will define a parabola in terms of its directrix and focus, graph para ...

http://www.ck12.org Chapter 9. Conics Notice how the three pointsP 1 ,P 2 ,P 3 are each connected by a blue line to the focus po ...