Oct. 31 Class

Today we talked about how to graph the exponential function.

Handouts:
Graphing Exponential Functions (page 1)
Graphing Exponential Functions (page 2-3)

An exponential function is a function of the form: .

Where b is any base that is greater than zero and not equal to 1 (forgot to mention that in class!  Remind me to tell everyone tomorrow.)

The graph of  looks like the following:

Where I've highlighted some important points that you might use to graph it.

Some important features of this graph include:

• Always increasing.
• Always above zero.
• As x becomes larger, y gets very large.
• As x becomes more negative, y gets closer to zero.
• Never touches the x-axis (a horizontal asymptote).

Next we graphed , and got,

Which turns out to be a horizontal reflection of the above graph.  Points to note:

• The reciprocal of the base is the same thing as a horizontal reflection.
• The y-intercept is always 1 for any base.

Lastly, if you had a table of values and tried to calculate the first and second differences, you will not be able to tell if it's an exponential function.  Instead you must calculate the ratios of each y-value to the y-value before it.  If the ratios are constant then you have an exponential function.

Homework:

Complete the page of the handout for .

P. 243 # 1 - 2.

Oct. 30 Class

I handed out the revised copy of the current unit's daily plan.

Handout: New Daily Plan for Unit 4

As we discussed the next test will be split up over two days.

Today we discussed how to simplify algebraic expressions with exponents.

Here are the notes and examples:

We also had a discussion about negative signs and radicals with negative radicands.

Homework: P. 235 # 4 – 12

Oct. 29 Class

Today we discussed what it means to have a rational exponent.  Through some discussions I showed that 8 with exponent 1/2 is the same thing as the square root of 8.

Here are my notes:

Homework: P. 226 #1-7(eoo), 11-14 (eoo)

Oct. 26 Class

New Unit: Exponential Functions

Today we began our new unit on exponential functions.  As a review we went over the important laws of exponents.

Handout: Exponent Review

Here are the notes:

Then I went over how to solve equations where the variable is in the exponent.

Here are the notes:

 

Homework: 

Complete the handout (every other question)

P. 221  #(1,2,4–9,11,13,14,16) – b,d,f,h only

Oct. 25 Class

Congratulations on completing your test today!

The new unit on exponential functions will begin tomorrow.

Oct. 24 Class

Today we discussed some review topics for the test:

2 double sided long pages.

You should be able to:

 - Find zeroes of quadratic equations

 - Find vertex of quadratic equations

 - Find the equation of the axis of symmetry

 - Find maximum or minimum

Techniques:

 - Complete the square

 - Formula (x = -b/2a)

 - Quadratic Formula

 - Factoring to find zeros

 - Averaging the roots

 - Partial factoring

Know how to simplify radicals.

Know how to determine the nature of the roots of a quadratic equation.

Know how to solve linear quadratic systems.

Know how to solve word problems.

 - Cost / Revenue / Profit type

 - Area type

 - Speed type

 - Projectile type

 - "Find the numbers" type

Here are some solutions to word problems that I worked out in class:

Good luck in your studies!

Oct. 23 Class

Today we went over the solutions for the quiz.  Here they are!

Reminder: Your summative test is in two days!  Make sure you can do all the quiz questions because the summative test will be more difficult.

Homework: P. 202 #1-23

Oct. 19 Class

Today we learned how to do quadratic regressions using a graphing calculator.  Here is the handout:

Handout: Graphing Calculator Problems

As promised, here is a blank copy of the formative quiz.

Handout: Formative Quiz

Oct. 18 Class

Today we complete a formative quiz!  Congratulations, I will have them marked and returned to you for Tuesday.

Then we discussed how to describe a family of quadratic functions.  Here are some notes I gave in class.

Here is an angry birds image that goes with the example above:

Homework: P. 192 #1-3, 4-5(eoo), 6-11, 14

Oct. 17 Class

Learning Goals: Understand how to find the intersection between a parabola and a line.

Here are some of the solutions from the word problems I handed out on previous days.  They are from the second page of the hand out.

And here are the new notes on the intersection between a linear function and a quadratic function.

Homework: Pg. 198 #1ac, 2ac, 3, 4ac, 6-13

Oct. 16 Class

Learning Goals: Solve word problems involving finding the maximum and minimum of quadratic functions.

Today we continued with word problems.  These word problems involve finding the maximum or minimum of quadratic functions.

Handout: Max/Min Word Problems

Here are the solutions to the examples I worked out in class.

Homework: Complete the second page of the handout (front and back!).

Oct. 15 Class

Today we began solving world problems involving quadratic functions.

Here is a handout: Zero word problems

All of these problems involve finding the zeroes of quadratic functions.  You must be able to

• Interpret the problem.
• Write a mathematical statement.  (Let statement if necessary.)
• Solve the problem by finding the zeroes.
• Interpret the solutions by writing a concluding statement.

Here are the solutions to the first few questions on the handout:

Page 55

1. (a) The ball was in the air for 4.1 seconds.

1. (b) The ball was above 17 m for 2 seconds.

2.  The tile is 3cm by 8 cm.

3.  The matte must be 10 cm wide.

Page 57 

1.  The numbers are 14 and 16 or they can also be -16 and -14.

2.  The two sides are 9 cm and 12 cm.

3.  The width of the strips must be 20 m.  (-120 is not physical.)

4.  The speed is 600 km/h.  (-700/13 is not physical.)

The solutions to the rest of the handout are printed at the bottom of the page.

Homework: 

g. 178 #6ac, 7-14

P. 185 #11, 13-16

Oct. 12 Class

Learning Goals: Review how to solve quadratic equations and determine the number of roots.

Today I gave two handouts involving different methods of solving quadratic equations.  The following are three methods:

• Factoring
• Quadratic Formula
• Completing the square and isolating for x

Factoring is perhaps the quickest if the equation is factorable.  The quadratic formula will always work so use that when factoring is not possible.  Completing the square is similar to the quadratic formula and you are expected to be able to use this method upon demand.

Handout: Solving Quadratic Equations

Handout: The Discriminant

Here are some solutions and notes I gave in class.

Homework: 

Pg. 177 #1, 2, 4, 5

Pg. 185 #1-4, 6-10

Oct. 11 Class

Learning Goals: Understand how to simplify radical expressions.

Today I discussed all the rules to simplify radicals.  This will be important when work with the quadratic formula.

Handout: Radicals

Here are the notes,

Homework:  P. 167 #1-7 (eoo), 8-13

Change in Test Date

I announced today that there is a change in the scheduling.  We will not be doing inverses since they were covered last unit, so each of topics will be shifted one day earlier.  That means the Unit 3 Test will be on Thursday, Oct. 25th.

Please make a note of it.

Oct. 10 Class

Learning Goals: Understand how to find the maximum and minimum value of quadratic functions.

Today I took you through the procedure to complete the square.  Then I discussed some shortcuts to find the vertex including partial factoring and using a formula.

Handout: Completing the Square

Here are the notes:

Homework: 

P. 153 #1-3,

#4abc (by completing the square), #4def (by averaging the zeros),
5, 7ac, 8, 9, 11, 12

Oct. 9 Class

Learning Goals: Understand information that can be extracted from different forms of quadratic functions.

Today we began the new unit on quadratic functions.  Much of this unit will look familiar to what you year learned in grade 10.  I took up some of the review today:

Quadratic Relationship Review

Here are some of the notes from class:

Tomorrow I will review how to complete the square and talk about partial factoring.

Homework: P. 458 #1-8, 9ace, 10-12, handout: Max and min of quadratic functions.