7.1 and 7.2 Graphing Inequalities 7.3 Solving Equations Using Quadratic Techniques Algebra II w/...

7.1 and 7.2 Graphing Inequalities7.3 Solving Equations Using Quadratic TechniquesAlgebra II w/ trig

•I. Vocabulary:

•A. Degree of a polynomial is the highest power of a polynomial.

•B. Leading coefficient is the number of the term with the highest degree.

•C. State the degree and leading coefficient of each one variable polynomial. If it is not a polynomial in one variable, explain.

1.

2.

3.

4.

4 26 3 4 8x x x

2 22x xy y

2 12 2

4a a

2 13 4 2c c c

II. Evaluate a Polynomial Function

A. Find

B. Find

3 4 3( ) ( ) 2 3p y ifp x x x x

2(2 1) 3 ( ) ( ) 2 1b x b x ifb m m m

C. Find

D. Find

2( ) ( ) 5 3f x h iff x x

2(3) ( 3) ( ) 2 4 6f f iff x x x

III. Graphs of Polynomial FunctionsA. Graphs of polynomial functions are

continuous.B. Graphs of polynomial functions have

only smooth turns. A function of degree n has at most n-1 turns.

C. If the leading coefficient is positive, the right side of the graph rises. If it is negative, the right side of the graph falls.

D. If the degree is even, the graph has the same end behavior on the left and right. If the degree is odd, the graph has opposite end behaviors on the left and right.

Degree: even Leading Coefficient: positive

Degree: Odd Leading Coefficient: positive

Degree: even Leading Coefficient: negative

Degree: Odd Leading Coefficient: negative

E. Describe the end behavior, determine if odd or even degree and state the number of real zeros.

1. 2.

3. 4.

•Factor completely and then graph.

5. 6. 21 xxxf )3(1 2 xxxxf

7. 8. 132 xxxxf 252 xxf

9. 10. xxxxf 44 23 234 20xxxxf

•7.3 Solving Equations Using Quadratic Techniques

 A. Solving Quadratics:

1. Factoring 

2. Quadratic Formula 

3. Square root method 

ExamplesSolve each equation.1. 2.010029 24 xx 02163 x

3. 4. 064

1

2

1

xx 010029 3

23

4

xx

HOMEWORK

•pg 350 #16-38 even and 39-44 all and 57 on page 352

•page 356 # 13 – 25 odd (find the end behavior only)

• page 157 # 65 – 77 odd, 87 – 93 odd (worksheet)

•page 363 # 17 – 26 all, 29, 30, 39