Lesson 9-6: Analyzing Solutions to Quadratic Equations
We have learned that we can use the discriminant in the quadratic equation (the value of the radicand, the stuff under the radical symbol) to determine if there are 2, 1 or 0 real solutions for a quadratic equation set to 0.
Watch the Virtual Nerd skillfully explain how this works.
How to tell if a quadratic equation has no real solution
The Virtual Nerd presents! She uses the quadratic formula to find the solution of a quadratic equation. Step one: set the equation = 0. That is: solve for x when y = 0.
After you have watched the video, go to the online calculator and enter the same equation she solved so you can see its graph.
Properties of Powers
We have learned 7 properties that help us to simplify expressions that include power functions. To review these properties, visit with our pal the Virtual Nerd. She demonstrates each property with examples:
Product of Powers Property
Quotient of Powers Property
Power of a Power Property
Power of a Product Property
Power of a Quotient Property
Negative Exponent Property
Lesson 11-5: Solving Systems by Multiplication
This powerpoint presentation will help you review the step-by-step process for solving a system of equations using multiplication and addition to eliminate a variable. The link will open a powerpoint file. Once you open the file, choose to view it as a Slide Show.
Solving Systems of Equations by Multiplication (elimination).
Lesson 11-8: Super groovy online graphing calculator
This graphing calculator allows you to quickly graph equations, inequalities, systems of equations and systems of inequalities.
Try it with the examples from Lesson 11-8 and your homework problems, too.
Desmos Graphing Calculator.
Exploring the graphs of linear inequalities.
This web site offers the opportunity to explore the graphs of linear inequalities. Use the online directions to learn how to change the inequality symbol and change the coordinates to get positive, negative, zero and undefined slopes. You should notice when to shade above the line and when to shade below the line. You should notice when the line is solid and when the line is dashed.
Interactive Linear Inequality Activity.
Lesson 7-6: Equations for Lines Through Two Points
Our pal on the Virtual Nerd does a nice job explaining how to write an equation in slope-intercept form for a line through two points. She finds the slope using m = (y2 - y1)/(x2 - x1). She then uses this slope and either point to find the y-intercept.
Virtual Nerd: writes an equation for a line through two points.
Using the Generic Rectangle to Factor Polynomials.
We have used the generic rectangle to factor polynomials of the form
ax^2 + bx + c where a is not equal to 1 (or 0).
NOTE: ax^2 means "a times x squared" and is written this way when it is not possible to write an exponent traditionally.
I have found 3 videos on youtube that use a VERY similar method, but they call it the "box" method. Each of these videos shows the steps needed to fully factor a trinomial. I recommend trying to factor the trinomials yourself and then watch the video to see how you did! I have ordered them in terms of difficulty. Click the links below to watch each video.
Algebra: Using FOIL and Area Model to multiply polynomials.
On this web site, there is a PowerPoint that demonstrates the FOIL and Area Model for multiplying polynomials.
If you are interested, go to the web site and look for the link that says "Notes: Multiplying Polynomials (ppt)" (or click the link here).
It is a PowerPoint and you can download it or open it to view.
Pearson Algebra Online.
Algebra: Video about multiplying polynomials (Lesson 10-4).
Use this video to review the process for using the Extended Distributive Property to multiply polynomials.
Multiplying polynomials videos.
Algebra: Video explaining FOIL (Lesson 10-5)
Use this video to review how the mnemonic FOIL can help you multiply binomials.
Lesson 2-2: Reciprocals
From Lesson 2-2: What is a reciprocal and how to find the reciprocal of a number: Reciprocals
Algebra: How to graph the intersection of two inequalities.
How to graph the intersection of two inequalities
Algebra: How to graph the union of two inequalities.
How to graph the union of an inequality.