quiz 2 math 112

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55 Terms

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[3.1]Exponents are used to…

Denote repeated multiplication

<p>Denote repeated multiplication</p><p></p>
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[3.1]Example of exponents

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[3.1]Powers of -1

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Exponent of 1

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Consider positive powers of 2…

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Negative Exponents

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Power of Product Rule

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Product rule

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Quotient Rule

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Power rule

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Simplifying with exponents

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[3.2] Factors

Real numbers, variables, or expressions multipled ( or divided ) together

<p>Real numbers, variables, or expressions <strong>multipled ( or divided )</strong> together</p>
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[3.2] Terms

Real numbers, variables or expressions added/subtracted Together

<p>Real numbers, variables or expressions <strong>added/subtracted </strong>Together</p><p></p>
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[3.2] Coefficient

The value multipled to a variable

<p>The <strong>value</strong> multipled to a variable</p>
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[3.2] Degree

The exponent of the variable

<p>The exponent of the variable</p>
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Like Term

Terms that share the same variables and variable exponents

<p>Terms that share the <strong>same variables and variable exponents</strong></p>
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Add/subtract like Terms by adding /subtracting their…

Coefficients

<p>Coefficients</p>
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Polynomials

expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)

Poly = Many

Nomials = Terms

<p><strong>expression of more than two </strong><a target="_blank" rel="noopener noreferrer nofollow" class="rMNQNe link" href="https://www.google.com/search?client=safari&amp;sa=X&amp;sca_esv=c603169f47c86d12&amp;hl=en-us&amp;biw=1128&amp;bih=1375&amp;sxsrf=AHTn8zqqRH2hSoOEo-vqNiK-YRXEvLbTjw:1746025295563&amp;q=algebraic&amp;si=APYL9bsF-Mq-fXaAyJcIV7GbwI1qPZFCtVIb4kUX5f-KXuqw6fn2O6SqWvmZu9DPwiKpirsZujngMZ03LzIMPhHyt68MP8m95yLyWTVcVRpf3y2C4c_meKc%3D&amp;expnd=1&amp;ved=2ahUKEwiX-YqMg4CNAxWGIjQIHaWJBWEQyecJegQIQxAS" data-prevent-progress="true"><strong><u>algebraic</u></strong></a><strong> terms, especially the sum of several terms that contain different powers of the same variable(s)</strong></p><p>Poly = Many </p><p>Nomials = Terms </p>
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Polynomials Standard Forms

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Degree of a Polynomial

The largest degree of the variables (aka :n)

<p>The largest degree of the variables (aka :n)</p>
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Distributive Property

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[3.2] Special cases of distributive property

Perfect Square Trinomial

  • Negative

  • Positive

Difference if Squares

<p>Perfect Square <strong>Trinomial</strong></p><ul><li><p>Negative</p></li><li><p>Positive</p></li></ul><p><strong>Difference if Squares</strong></p>
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[3.2] Polynomial operations

Replace the function notation with the function definition.

<p>Replace the function notation with the function definition.</p>
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[3.2] Factoring

Is the process of undoing distribution ( turning sums into products of sums )

There are two types!

  • Expanded forms

  • Factored forms

<p>Is the process of <strong>undoing distribution</strong> ( turning sums into products of sums )</p><p>There are two types!</p><ul><li><p>Expanded forms</p></li><li><p>Factored forms</p></li></ul>
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[3.2] Process of Factoring

We need to find A and B we will use “restricted guess and check

  • Guessing and checking values within certain parameter

<p>We need to find <strong>A</strong> and <strong>B</strong> we will use “<strong>restricted guess and check</strong>”</p><ul><li><p>Guessing and checking values within certain parameter</p></li></ul>
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[3.2]What if the coefficient of 𝒙𝟐 is not 1?

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[3.2] GCD !

Greatest common Divisor of two terms is the largest factor shared between both terms

Only do this is possible

<p>Greatest common Divisor of two terms is the largest factor shared between both terms</p><p>Only do this is possible</p>
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[3.2] What If factorization is possible?

If a polynomial cannot be factored it is considered to be prime

<p>If a polynomial cannot be factored it is considered to be prime</p>
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[3.2] Factoring by grouping!

If you rewrite the polynomial, you may be able to factor out the GCD.

<p>If you rewrite the polynomial, you may be able to factor out the GCD.</p>
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[3.2] ABC method!

<p></p>
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[3.2] Example of ABC method

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[3.2] Special factoring techniques: Perfect Square Trinonial

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[3.2] Special Factoring :Different of squares

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[4.1] a quadratic function has the general form…

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[4.1]The graph of quadratic function are called..

Parabolas

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[4.1] quadratic function graphs look like

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[4.1] Quad-Ratic

Largest term is Square. Square has 4 sides ( reminder )

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[4.1] properties of Parabolas

Vertex, vertical and horizontal intercept and Concavity.

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[4.1] Vertex

Its the point whose y-value is either less than or greater than the y - values of all the other points

The lowest or the highest

<p>Its the point whose y-value is either less than or greater than the y - values of all the other points</p><p>The lowest or the highest</p>
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<p>[4.1] if the parabola opens UP ( U shape ) then it is…(concavity)</p>

[4.1] if the parabola opens UP ( U shape ) then it is…(concavity)

Concave Up

<p>Concave Up</p>
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<p>[4.1] ( Concavity ) if the parabola opens down then it is is..…</p>

[4.1] ( Concavity ) if the parabola opens down then it is is..…

Concave down

<p>Concave down</p>
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[4.1] Vertical intercept…

Parabolas will always have just 1 vertical intercept

<p>Parabolas will always have just<strong> 1 vertical intercept</strong></p>
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[4.1] horizontal intercept ….

Parabola may have… 0 1 or 2 horizontal intercepts

<p>Parabola may have… 0 1 or 2 horizontal intercepts</p>
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[4.1] how to know if something is a quadratic function…

Knowing if the quadratic function is up or down but If it isn't either then it isn't one

<p>Knowing if the quadratic function is up or down but If it isn't either then it isn't one</p>
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[4.1]Another example of quadratic functions

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[4.1] Zero Factors

If a product equals zero then at least the factor must be Zero

If ab=0 then A= 0 and/or b= 0

<p>If a <strong>product</strong> equals zero then at least the <strong>factor</strong> must be Zero</p><p>If ab=0 then A= 0 and/or b= 0</p>
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[4.1] the horizontal interception(s) of a quadratic fiction occurs when…

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[4.1] the horizontal interceptions for solving quadratic equations are also called..…

“Zeroes” and “roots” of the polynomial

<p>“Zeroes” and “roots” of the polynomial</p>
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[4.1] Word problem for solving quadratic equations

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[4.1]Square Root

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[4.1] getting two values from the same operations is not ideal so….

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[4.1] Square Root Property

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[4.1] Solving for variable inside bases

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[4.1] Perfect Square Trinomials

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[4.1] Completing the Square

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