About This Chapter
First, what are parabolas, and where do we see them in real life? As you journey along this learning curve, you'll learn how to identify a parabola's key attributes: vertex, maximum, roots and axis of symmetry. You'll also encounter parabolas in their standard, vertex and intercept forms. By the time we're done, you'll view these strange creatures as familiar friends and know how to answer even the most abstract questions about them.
Only marathon runners and inept mathematicians take the long way, so we'll teach you a shortcut with the FOIL method. No, it doesn't involve wrapping up leftovers before putting them in the fridge; instead, it's a speedy way to multiply two binomials. As you get more practice, you'll also see how the area method can help with multiplying more complex polynomials.
In some mathematical cases, you'll need to move from a polynomial to a product, or from standard form to intercept form. You'll see how factoring makes this possible. Along the way, you'll encounter the diamond problem and learn how to factor by grouping. We also have plenty of practice problems, so you can get comfortable with completing the square when it comes to quadratic equations.
Last but not least, you'll use your factoring expertise to solve quadratic equations. We'll give you all the information and tools that you need to succeed, such as the zero product property, discriminants and the quadratic formula. By the end of these videos, you'll even know how to solve quadratics that aren't written in standard form. We're making algebra accessible, one great lesson at a time.
1. What is a Parabola?
A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.
2. Parabolas in Standard, Intercept, and Vertex Form
By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.
3. Multiplying Binomials Using FOIL and the Area Method
From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most.
4. Multiplying Binomials Using FOIL & the Area Method: Practice Problems
There are a few mistakes that are easy to make when multiplying binomials with FOIL and also a few ways to complicate problems like this, so why not make sure you're brushed up on your skills? You'll also learn a shortcut and how to use the area method to multiply even bigger polynomials.
5. How to Factor Quadratic Equations: FOIL in Reverse
So, you know how to multiply binomials with the FOIL method, but can you do it backwards? That's exactly what factoring is, and it can be pretty tricky. Check out this lesson to learn a method that will allow you to factor quadratic trinomials with a leading coefficient of 1.
6. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient
Once you get good at factoring quadratics with 1x squared in the front of the expression, it's time to try ones with numbers other than 1. It will be the same general idea, but there are a few extra steps to learn. Do that here!
7. How to Complete the Square
Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here.
8. Completing the Square Practice Problems
Completing the square is one of the most confusing things you'll be asked to do in an Algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here!
9. How to Solve a Quadratic Equation by Factoring
If your favorite video game, 'Furious Fowls,' gave you the quadratic equation for each shot you made, would you be able to solve the equation to make sure every one hit its target? If not, you will after watching this video!
10. How to Use the Quadratic Formula to Solve a Quadratic Equation
When solving a quadratic equation by factoring doesn't work, the quadratic formula is here to save the day. Learn what it is and how to use it in this lesson.
11. How to Solve Quadratics That Are Not in Standard Form
It isn't always the case that your equation will be set up nicely for you to solve. In this lesson, learn how to factor or use the quadratic formula to solve quadratic equations, even when they are not in standard form.
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Other chapters within the Math 101: College Algebra course