Chapter 2 Polnomial and Rational Functions Course Number Section 2.1 Quadratic Functions and Models Instructor In this lesson ou learned how to sketch and analze graphs of functions. Date Define each term or concept. a aaaa aaaaa aaaaa a aaaaaaaa aa aaaaaaaaaa aaaa aaaaaa aaa aaaa aa aaaaaaaaa aaa aaaaa aaaaa aaa aaaa aaaaaaaaaa aaa aaaaaaaaa Letn be a nonnegative integer and let a n,a n 1,..., a 2,a 1,a 0 be real numbers with a n 0. A of with degreen is... aaa aaaaaaaa aaaa a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a How to analze graphs of quadratic functions Leta,b, and c be real numbers with a 0. A is... aaa aaaaaaaa aaaa a aa a a aa a aa A quadratic function is a polnomial function of aaaaaa a degree. The graph of a quadratic function is a special U -shaped curve called a aaaaaaaa. If the leading coefficient of a quadratic function is positive, the graph of the function opens aaaaaa and the verte of the parabola is the aaaaaaa -value on the graph. If the leading coefficient of a quadratic function is negative, the graph of the function opens aaaaaaaa and the verte of the parabola is the aaaaaaa -value on the graph. The absolute value of the leading coefficient determines aaa a aaaaaa aaa aaaaaaaa aaaaa. If a is small, aaa aaaaaaaa aaaaa aaaa aaaaaa aaaa aa a a a aa aa a aaaaaaa a 31
32 The is aaaa a aaa a aa a a aaa a a. For a quadratic function in standard form, the ais of the associated parabola is a a a and the verte is aaa aa. How to write quadratic functions in standard form and use the results to sketch graphs of functions To write a quadratic function in standard form,... aaaaaaa aa aaaaaaaaaa aaa aaaaaa aa aaa aaaaaaaa aa aaa aaa To find the -intercepts of the graph of aaaaa aaa aaaaaaaa aa a a aa a a a aa 2 f ( ) = a + b+ c,... Sketch the graph of f ( ) = + 2 8 and identif the verte, ais, and -intercepts of the parabola. aa aa a aaa a a a aa aa aa aa aaa aaa aa 2 For a quadratic function in the form 2 f ( ) = a + b+ c, the -coordinate of the verte is given as a aaaaaa and the -coordinate of the verte is given as aaaaaaaaaa. How to use quadratic functions to model and solve real-life problems Find the verte of the parabola defined b 2 f ( ) = 3 11+ 16. aaaaaa aaaaaa Page(s) Eercises
33 Section 2.2 Polnomial Functions of Higher Degree Objective: I. Graphs of Polnomial Functions g f f aaa II. The Leading Coefficient Test Leading Coefficient Test. a aaa a a a a aa a a Eample: Important Vocabular Continuous Repeated zeroaa a aaa Test intervals Intermediate Value Theoremaaaaa aaaaaaa aaaa f
34 III. Zeros of Polnomial Functions fnf af a fa f aaa aaaa aaaa aaa f f f f Eample : f IV. The Intermediate Value Theorem f aaaaaaa aaaaaaaaa aaaaaa f aaa aaaa aa Homework Assignment
35 Section 2.3 Polnomial and Snthetic Division aaaaaa aa aaaaaa aa fd rdf aaa a aa aa aa k
36 aa aaaaa fk aaaaaa f aa aaaa k f aaaaa aaaaa aa r f k aaaaaaa aaaaa aaaa
37 Section 2.4 Comple Numbers In this lesson ou learned how to perform operations with comple numbers. Course Number Instructor Date Define each term or concept. aaa aaa a aaa aaaa aaaaaaaa aaa aaaaaa a a aaa aaaaa aaa aaaaaa a aa aaaaaa aaa aaaa aaaa aaa aaa aaaaaa aa aa aaaaaa aaa aaaaaaaaa aaaaa aa a aaaaaaa aaaaaa aaaaaaa aa aaaaaaaa aaaaa aaa a aa aaa aaaaaa a a aa aa aaaaaa aa aaaaaaaaa aaaaaaa a aaaa aa aaaaaaa aaaaaaa aa aaa aaaa a a aa aaa a a aaa i Mathematicians created an epanded sstem of numbers using the i defined as i = a a a, because... aaaaa aa aa aaaa aaaaaa a aaaa aaa aa aaaaaaa aa aaaaaaa a aa How to use the imaginar uniti to write comple numbers B definition, i 2 = a a. For the comple number a + bi, if b = 0, the number a + bi = a is a(n) aaaa aaaaaa. If b 0, the number a + bi is a(n) aaaaaaaaa aaaaaa.if a = 0, the number a + bi = bi is a(n) aaaa aaaaaaaaa aaaaaa. The set of comple numbers consists of the set of aaaa aaaaaaa and the set of aaaaaaaaa aaaaaaa. Two comple numbers a + bi and c + di, written in standard form, are equal to each other if... aaa aaaa aa a a a aaa a a aa To add two comple numbers,... aaa aaa aaaa aaaaa aaa aaa aaaaaaaaa aaaaa aa aaa aaaaaaa aaaaaaaaaaa How to add, subtract, and multipl comple numbers To subtract two comple numbers,... aaaaaaaa aaa aaaa aaaaa aaa aaa aaaaaaaaa aaaaa aa aaa aaaaaaa aaaaaaaaaaa
38 The in the comple number sstem is a. The of the comple number a + bi is a aa a aaa a a a a aa. Perform the operations: (5 6i) (3 2i) + 4i a To multipl two comple numbers a + bi and c + di,... aaa aaaaaaaaaaaaaa aaaa aaa a aaa a aaa a aaaa aa aaa aaa aaaaaaaaaaaa aaaaaaaa aa aaaaaaaa aaa aaa aaaaaaa aaaaaaaa aaa aaaaaaa aa aaaaa aaa aaaa aaaaaa aaa aaaaaaaaaaa aaa aaaaaaaaa Multipl: (5 6i)(3 2i) a a aaa The product of a pair of comple conjugates is a(n) aaaa number. To find the quotient of the comple numbers a + bi and c + di, wherec and d are not both zero,... aaaaaaaa aaa aaaaaaaaa aaa aaaaaaaaaaa aa aaa aaaaaaa aaaaaaaaa aa aaa aaaaaaaaaaaa How to use comple conjugates to write the quotient of two comple numbers in standard form Divide (1 + i) b (2 i). Write the result in standard form. aaa a aaaa Ifa is a positive number, the of the negative number a is defined as a a a a a a a. How to find comple solutions of quadratic equations To avoid problems with multipling square roots of negative numbers, be sure to convert to aaaaaaaa aaaa before multipling.
39 Perform the operation and write the result in 2 standard form: ( 5 4) aa a aaa Page(s) Eercises
40 Precalculus, Sith Edition
41 Section 2.5 Zeros of Polnomial Functions n a f aa aaaa aaa a aa aa aa a a a a a n a aa aa aa aa
42 aaa a a a a a a a a a a aa a aaaa aa a a a f f abib aaa n
43 f aaaaaaaa aa a aaa a a a a a a a a a a aa a a aa a aa k a
44 f f aaaaa aaaaa aa aaaa a a aa aa
45 Section 2.6 Rational Functions a aa f aa a f aa a aa aaaaaa aaaaaa aaaaa aaaa aaa aaaaa
46 f n n N an an L a a f D m m bm bm L b b ND f aa f aa aa nmfa a nmf aa a a a nmf f aaa fnd ND aa aaa aa a
47 f f f aa
48
49 Section 2.7 Nonlinear Inequalities a a a a a
50 + < aa a a + >
51 + R= C = + R C a
52