Parabolas Ep. 4 - Looking at Parabolas When a is a Fraction - 10:07

Factoring Ep.1: Guideline to Factoring - 6:34

KEY CONCEPTS:

First step to factoring, is to find a common factor.

After that, regardless of whether there is a common factor or not is to count the number of terms.

Based on that will determine how to Factor

Polynomials Ep. 8: Special Products (a+b)2 - 6:13

KEY CONCEPTS:(a+b)^2 = a^2+2ab+b^2

- square your a value - first term of your Perfect Square Trinomial
- square your b value - third term of your Perfect Square Trinomial
- multiply your a and b value together and then multiply that value by 2 to get your middle term of your trinomial

Polynomials Ep. 7 - Multiplying Binomials

KEY CONCEPTS:

F.O.I.L Method - First - Outer - Inner - Last

Multiplying binomials form trinomials

Parabolas Episode 9 - The Vertex Form of Quadratic Functions (h,k) - 21:12

Parabolas Ep. 7 - Introduction of the (0,k) Vertex Form - 22:38

KEY CONCEPTS:

In this video we see how Quadratic Function written in the form of:

y=ax^2+k - will lead us to a vertex of (0,k)

Parabolas Ep. 6 - Using the 1,3,5-Pattern for Graphing - 11:30

KEY CONCEPTS: In this video we look at the 1,3,5-Pattern for graphing quadratic function (parabolas). These videos are intended for the viewer to steer away from using Table of Values and to use the Vertex form along with the 1,3,5-Pattern.

How did we come up with the 1,3,5-Pattern? Look closely at the differences in the y-axis.

Parabolas Ep. 2 - The Quadratic Function - 4:16

KEY CONCEPTS:

The following video looks at the various ways that quadratic functions can be written. Be on the lookout for such equations, because if you ever come across them you'll know they form a parabola.

Parabolas Ep. 11 - Steps to Completing the Square - 13:32

KEY CONCEPTS:

Completing the Square involves converting a quadratic function from STANDARD FORM into a VERTEX FORM.

Steps:
1. Group the x's together and keep the constant (c-value) off to the side.
2. Factor the a-value from x^2 and x (IF we have an a-value)
3. Divide the x-value by 2 and then square it.
4. With the value you get from Step 3, add it to your x^2 and x value and subtract it by that same value (don't forget about the c-value - we're not using it yet, until the end)
5. The first 3 terms you have form a Perfect Square Trinomial (P.S.T) - Factor your P.S.T by square rooting your first term of the PST and the third term of the PST
6. Create your binomial of squares (Special Products)
7. Multiply your a-value (IF you factored one out) with the minus value from Step 4.
8. Simplify the number from Step 7 with the c-value we set aside at the start.

Parabolas Episode 10: Completing the Square - 24:40

KEY CONCEPTS:

Completing the Square involves converting a quadratic function from STANDARD FORM into a VERTEX FORM.

Steps:
1. Group the x's together and keep the constant (c-value) off to the side.
2. Factor the a-value from x^2 and x (IF we have an a-value)
3. Divide the x-value by 2 and then square it.
4. With the value you get from Step 3, add it to your x^2 and x value and subtract it by that same value (don't forget about the c-value - we're not using it yet, until the end)
5. The first 3 terms you have form a Perfect Square Trinomial (P.S.T) - Factor your P.S.T by square rooting your first term of the PST and the third term of the PST
6. Create your binomial of squares (Special Products)
7. Multiply your a-value (IF you factored one out) with the minus value from Step 4.
8. Simplify the number from Step 7 with the c-value we set aside at the start.
9 Now you have your equation in VERTEX FORM.

Parabolas Episode 8 - Introduction of the (h,0) Vertex Form - 21:02

KEY CONCEPTS: This video looks at Quadratic Function written in the form:

y=a(x-h)^2 - where the vertex is (h,0)

**NOTE: When writing the x-value of the vertex, take the opposite sign of what's within the brackets. (i.e. y=2(x+3)^2 would give us a vertex of (-3,0)

Parabolas Ep. 5 - Looking at Parabolas that Reflect the x-Axis - 9:32

Parabolas Ep. 3 - Looking at the Differences in Simple Quadratic Expressions - 39:34

KEY CONCEPTS:

The following podcasts investigates table of values for quadratic functions. Understanding that difference we can graph other quadratic functions without the need to complete a table of values.

Parabolas Episode 1 - Who Cares About Parabolas - 2:34

This short video just looks at how parabolas are everywhere.

Factoring Ep.5: Factor Quadratics (Trinomials), a not = 1 - 10:16

KEY CONCEPTS:

Notice that your trinomial is a quadratic function, where the value of a is NOT equal to 1.

Use the sum-product rule
i.) find 2 numbers that multiply to your "a" and "c" value, that ALSO ADD up to your "b" value.
ii.) expand your middle term
iii.) factor by grouping
iv.) answer should be a set of binomials

Polynomials Ep. 9 - Special Products (a-b)2 - 5:49

Polynomials Ep. 6 - Dividing Monomials - 3:26

KEY CONCEPTS:

same rules apply like when multiplying monomials, except that we are dividing. Also remember the exponent rule, when powers have the same base, subtract the exponents.

Polynomials Ep. 5 - Multiplying Monomials - 5:30

KEY CONCEPTS:

When multiplying monomials, multiply:

- numbers with numbers
- same letters with same letters

**NOTE: When multiplying the letters with one another keep in mind the exponent rule for multiplying powers with the same base (ADD the exponents)

Polynomials Ep. 4 - Subtracting Polynomials - 5:32

KEY CONCEPTS:

When subtracting polynomials, distribute the negative from outside of the brackets by REVERSING the signs of all the terms within the brackets.

Polynomials Ep. 3 - Adding Polynomials - 5:42

KEY CONCEPTS:

Since the function outside of the SECOND set of brackets is a positive you can simply remove the brackets and collect like terms.

LIKE TERMS: terms that have the same variable (letter) as well as the same exponent. When adding the like terms, simply add the numbers in front and keep the variable (letter) the same (i.e. 3x+5x = 8x)

x, 7x, 9x, -3x are like terms with one another. 6x^2 is NOT a like term with the previous examples because of the exponent 2 found with the variable x.