3/29

I. Solving Statements of Equality Graphically.

  The intersection is the solution.

   

    If there is an intersection of the two graphs, there is a solution.

 

    If there is no intersection of the two graphs, there is no solution.

 

II. Solving Statements Graphically.

    If the statement is an inequality, the solution may be one or more intevals of numbers.

 

Ex. 1:     Solve:    |x - 2| < 1

    Translation: When is the distance from 2 less than 1?

    Answer:   Within one unit of 2: 1 < x < 3.

 

 

Ex. 2:     Solve:    |x - 2| > 1

    Translation: When is the distance from 2 greater than 1?

    Answer:   When the number is more than 1 than 1 unit from 2 in either direction: x < 1 or x > 3.

 

 

pg 226 #29, 30, 46, 37

Quiz on thursday the 6th, test on the 11th.

4/04

I. Sketch

1. odd function    2. even function

3. x     4. x²

5. x³    6. x⁴

Use your calculator to verify your answer.

II. Solve

7. x² = 4x - 5

8. x² - 7 = 0

9. x⁴ + 2x² + 1 = 0

Answer

III. Vocabulary: polynomial

linear

    y= ax + b

quadratic

    y = ax² + bx + c   or     y = a(x - h)² + k

cubic

    y = ax³ + bx² +cx + d

quartic

    y = ax⁴ + bx³ + cx² + dx + e

IV. The use of a quadratic to express displacement, see page 209, ex. 13

4/06

I. On the same plane graph y= (x - 1)² and y = x.

II. Sketch

2. y = - x⁵ + ...

3. y = x⁴ + ...

Consider the graphs of x³, 2x³, -2x³, x⁴, - x⁴, and the impact of the coefficient and power on the shape of the curve.

III. Vocabulary: end behavior, zeros, dilation, polynomials

IV. Polynomial Functions

    At dilation, see "A Line Dilated by A Line Yields A Quadratic."

    At Polynomial Graphs, see how the factors of a polynomial determine its behavior and therefore its graph.

V. Quiz answers.

VI. Test on the 11th.