Tuesday, February 3, 2009

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

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Thursday, January 29, 2009

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

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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

Tuesday, January 27, 2009

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

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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

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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

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

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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

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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

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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.

Monday, January 26, 2009

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

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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

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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

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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

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

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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

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This short video just looks at how parabolas are everywhere.

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

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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

Sunday, January 25, 2009

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

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Polynomials Ep. 6 - Dividing Monomials - 3:26

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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

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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

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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

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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.

Polynomials Ep. 2 - Distributive Law - 3:32

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KEY CONCEPTS:

Multiply the outside value (term) with EVERYTHING inside of the brackets.

Polynomials Ep. 1 - Types of Polynomials - 4:42

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KEY CONCEPTS:

7x
- the 7 represents the numerical coefficient
- the x represents the variable (literal coefficient - the unknown)
- together they would be multiplied together

Monomial - consists of one term (i.e. 7x, 5y^2, -3)

Binomial - consists of two terms (i.e. 2x-5, 3y^2 + 5y)

Trinomial - consists of three terms (i.e 3x^2-4x+7)

Thursday, January 15, 2009

Factoring Ep.7: Factor Difference of Squares - 7:19

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KEY CONCEPTS:

Difference of squares are binomials with the function of subtraction separating the 2 terms. NEVER a positive value.

When Factoring such special quadratics:
i.) square root the first term and the second term
ii.) place the first value as the first term of 2 sets of binomials and the second value as the second term
iii.) in one set of binomials write a negative, and the second set a positive.

ie. x^2-81 = (x+9)(x-9)

Factoring Ep.4: Factor Quadratics (Trinomials), a=1 - 13:53

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KEY CONCEPTS:

Factoring trinomials in the form of x^2+bx+c

i.) Find SUM-PRODUCT: ac-value and b-value
ii.) Square root x^2 value and open up a set of binomial brackets
iii.) Write x (or whatever variable is squared as your trinomials first term) as your first term in both brackets
iv.) Write your SUM-PRODUCT numbers as the second variables in each set of binomials

Factoring Ep.3 - Factor by Grouping - 9:50

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KEY CONCEPTS:

This works only with 4 term polynomials

STEPS:
i.) Find a common factor from all 4 terms
ii.) Group the first 2 terms and then the last 2 terms
iii.) Find common factor from first group
iv.) Find common factor from second group
v.) Factor out the common factor (bracketed terms)
vi.) Answer will be a set of binomials being multiplied together
vii.) Check your answer by expanding your answer.

Saturday, January 3, 2009

Polynomials Ep.11: Area Perimeter & Polynomials - 5:33

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KEY CONCEPTS:

Area = length * width

Perimeter = add ALL sides together

Polynomials Episode 10: Difference of Squares - 5:26

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KEY CONCEPT:

(a-b)(a+b) = a^2-b^2

Since the middle terms equals zero, of the FOIL method all we need to do it the First and the Last.

**NOTE:
we subtract the first squared value with the second.