WEEK 5 Day 2

Chapter 4 Equations and Their Graphs Functions and their equations can be graphed. Page 145

5 = 2x + 1x = 2 y = 2x + 1 x, y 2, 5 3, 7 4, 9

4.2 GRAPHING EQUATIONS page 152 Plotting points from order pairs. Plotting is fundamental to correct graphs.

From (ordered) pairs to plotting points to graphing.

Page 154 Solving for x = 0 This graphically means finding the point or points, if any, where the graph crosses the y axis. x y (0, 2)

4.3 THE STRAIGHT LINE Page 162 Y intercept may be solved mathematically. (section 4.3)

4.3 THE STRAIGHT LINE page 159 The slope of a line.

Any 2 ordered pair can be used.

4.3 THE STRAIGHT LINE page 161 This allows us to find the equation for a line given the slope of the line and a point (ordered pair).

For a line with point: (-1, 2) and a slope of: 3

4.5 THE DISTANCE AND MIDPOINT FORMULAS page 170

X, Y 2, 2 6, 5

Chapter 5 Factoring and Algebraic Fractions 5.1 Special Products 5.2 Factoring Algebraic Expressions 5.3 Other Forms of Factoring 5.4 Equivalent Fractions

Chapter 5 Factoring and Algebraic Fractions 5.5 Multiplication Division of Algebraic Expression 5.6 Addition and Subtractions of Algebraic Expressions 5.7 Complex Fractions 5.8 Equations with Fractions

5.1 Special Products

5.1 SPECIAL PRODUCTS page 181 There are two general forms of the square of a binomial. A binomial is an algebraic expression containing exactly two terms.

5.1 SPECIAL PRODUCTS page 181 Why is there no yx or xy ?

5.1 SPECIAL PRODUCTS page 182 There are two general forms of the cube of a binomial. Not for us

5-2 Factoring Algebraic Expressions

A product is the result obtained by multiplying two or more quantities together. Factoring is finding the numbers or expressions that multiply together to make a given number or equation.

5.2 FACTORING ALGEBRAIC EXPRESSIONS page 183

Greatest or largest.

5.2 FACTORING ALGEBRAIC EXPRESSIONS Greatest or largest common factor. 15ab – 6ac = 3a (5b – 2c)

5.2 FACTORING ALGEBRAIC EXPRESSIONS page 184

page 185 A summary about the signs in trinomials. If the trinomial to be factored is one of the following forms, use the corresponding sign patterns.

page 185

Middle term coefficient from addition (subtraction). Last term from multiplication.

page 186

From section 5.2

page 188 When the factors of a trinomial are the same two binomial factors, the trinomial is called a perfect square trinomial.

Page 188 And we have come back to the beginning.

5.3 OTHER FORMS OF FACTORING page 189 Some algebraic expressions may be factored by grouping their terms so that they are of the types we have already studied. Move on to section 5.4

5.4 Equivalent Fractions

5.4 EQUIVALENT FRACTIONS page 189 Two fractions are equivalent when both the numerator and the denominator of one fraction can be multiplied or divided by the same nonzero number in order to change one fraction to the other. a/a = 1

5.4 EQUIVALENT FRACTIONS page 192 A fraction is in lowest terms when its numerator and denominator have no common factors except 1.

5.4 EQUIVALENT FRACTIONS page 194 If you can do this You can do this

5.4 EQUIVALENT FRACTIONS page 194 Then this:

5.5 Multiplication Division of Algebraic Expressions

5.5 MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTIONS page 195 This is good.

5.5 MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTIONS page 195 Factor each of the terms in the numerator and denominator. Divide by common factors. Then multiply the numerators and denominators.

5.5 MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTIONS page 195

Doug’s technique.

Reorganize like terms.

60 a y 30 b x 2ay 1bx 2ay bx

5.5 MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTIONS page 195 You can never be too good at this.

Page 196

5.6 Addition and Subtractions of Algebraic Expressions

5.6 ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS page 198 Fractions may be added or subtracted if they have a common denominator. That is why a Least Common Denominator (LCD) must be determined.

5.6 ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS page 198 Denominators get factored.

A prime number is a positive that is evenly divisible only by itself and one. The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

5.6 ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS page 198 Factoring with prime numbers.

5.6 ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS page 198 Notice 540 is greater (larger) then any denominator and we are looking for Least Common Denominator.

5.6 ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS page 199

5.6 ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS page 198 Fractions may be added or subtracted if they have a common denominator. That is why a Least Common Denominator (LCD) MUST be determined. That is why a Least Common Denominator (LCD) SHOULD be determined. That is why a Common Denominator (CD) MUST be determined.

A common denominator by multiplying the denominators.

A common denominator

5.7 Complex Fractions 5.8 Equations with Fractions

5.7 COMPLEX FRACTIONS page 202 A complex fraction is a fraction that contains a fraction in the numerator, the denominator, or both.

5.8 EQUATIONS WITH FRACTIONS page = 2 x 2 x 3 6 = 2 x 3 8 = 2 x 2 x 2 2 occurs at most 3 times. 3 occurs at most once. 2 x 2 x 2 x 3 = 24 LCD = 24

5.8 EQUATIONS WITH FRACTIONS page 205

Check: Substitute 1 for x each time it occurs in the original equation.

R does not equal r. Solve for r.

R does not equal r. Solve for r.

R does not equal r. Solve for r.