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Algebra 2

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Rational & Root Equations

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Quadratic Systems

Awesome Math Tricks: Vertex Form, Difference of Cubes, and Sines and Cosines

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Awesome Math Tricks: Vertex Form, Difference of Cubes, and Sines and Cosines
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Shreeya Ram

@shreeyaram_iuea

·

19 Followers

Follow

A comprehensive guide to essential mathematical formulas and concepts, focusing on quadratic equations, trigonometry, and advanced algebraic operations. The material covers fundamental principles used in calculus and advanced mathematics.

  • Detailed coverage of vertex form of a quadratic equation examples and variations
  • In-depth exploration of algebraic concepts including the difference of cubes formula explanation
  • Practical law of sines and cosines applications for triangle calculations
  • Essential formulas for exponential growth, logarithms, and trigonometric functions
  • Advanced probability concepts including permutations and combinations

7/25/2023

118

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

View

Page 2: Advanced Algebraic Forms and Functions

This page delves into more complex algebraic forms including polynomial functions, difference of cubes, and exponential expressions.

Definition: The difference of cubes formula states that a³-b³ = (a-b)(a²+ab+b²)

Example: The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius

Highlight: Polynomial functions can be written in factored form as f(x) = a(x−p)(x−q)(x−r) where p, q, and r are the roots

Vocabulary: A fractional exponent can be converted to a radical form, where a^(1/n) = ⁿ√a

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

View

Page 3: Exponential and Logarithmic Functions

This page covers exponential growth, decay, and logarithmic functions, with applications in compound interest and half-life calculations.

Definition: Compound interest formula: A = P(1 + r)ⁿ, where A is final amount, P is principal, r is interest rate, and n is number of periods

Example: For continuous compound interest, the formula A = Pe^(rt) is used, where e is Euler's number

Highlight: The half-life formula N(t) = N₀(1/2)^(t/t₁/₂) is crucial in radioactive decay calculations

Vocabulary: Asymptotes are lines that a curve approaches but never touches, defined by x = h and y = k in hyperbolic functions

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

View

Page 4: Trigonometric Functions and Probability

This page explores trigonometric relationships and probability calculations, including the laws of sines and cosines.

Definition: The law of cosines states that a² = b² + c² - 2bc cos(A) for any triangle

Example: The area of any triangle can be calculated using A = de sin(f), where d and e are sides and f is the included angle

Highlight: Permutations (P(n,r) = n!/(n-r)!) calculate arrangements where order matters

Vocabulary: The law of sines relates side lengths to angles: sin(A)/a = sin(B)/b = sin(C)/c

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

View

Page 5: Advanced Mathematical Concepts

This page concludes with advanced mathematical concepts and specialized formulas for probability and trigonometric calculations.

Definition: The probability formula for multiple selections involves combinations and specific conditions

Example: Vertical shifts in trigonometric functions are represented by adding or subtracting constants

Highlight: The tangent function V = tan(θ) relates to the ratio of sine and cosine

Vocabulary: Probability calculations often involve combinations (C(n,r) = n!/(r!(n-r)!)) for selecting items where order doesn't matter

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

View

Page 1: Essential Algebraic Formulas

This page introduces fundamental algebraic equations and formulas essential for mathematical problem-solving. The content focuses on various forms of linear and quadratic equations.

Definition: The quadratic formula is used to find the roots of any quadratic equation: x = (-b ± √(b² - 4ac))/2a

Example: To find the axis of symmetry of a parabola, use the formula -b/2a

Highlight: The vertex form of a quadratic equation, f(x) = a(bx – h) + k, is particularly useful for graphing parabolas and finding maximum/minimum points

Vocabulary: Slope-intercept form (y = mx + b) represents a linear equation where 'm' is the slope and 'b' is the y-intercept

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Subjects

/

Algebra 2

/

Rational & Root Equations

/

Quadratic Systems

Awesome Math Tricks: Vertex Form, Difference of Cubes, and Sines and Cosines

user profile picture

Shreeya Ram

@shreeyaram_iuea

·

19 Followers

Follow

A comprehensive guide to essential mathematical formulas and concepts, focusing on quadratic equations, trigonometry, and advanced algebraic operations. The material covers fundamental principles used in calculus and advanced mathematics.

  • Detailed coverage of vertex form of a quadratic equation examples and variations
  • In-depth exploration of algebraic concepts including the difference of cubes formula explanation
  • Practical law of sines and cosines applications for triangle calculations
  • Essential formulas for exponential growth, logarithms, and trigonometric functions
  • Advanced probability concepts including permutations and combinations

7/25/2023

118

 

9th/10th

 

Algebra 2

3

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

Page 2: Advanced Algebraic Forms and Functions

This page delves into more complex algebraic forms including polynomial functions, difference of cubes, and exponential expressions.

Definition: The difference of cubes formula states that a³-b³ = (a-b)(a²+ab+b²)

Example: The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius

Highlight: Polynomial functions can be written in factored form as f(x) = a(x−p)(x−q)(x−r) where p, q, and r are the roots

Vocabulary: A fractional exponent can be converted to a radical form, where a^(1/n) = ⁿ√a

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

Page 3: Exponential and Logarithmic Functions

This page covers exponential growth, decay, and logarithmic functions, with applications in compound interest and half-life calculations.

Definition: Compound interest formula: A = P(1 + r)ⁿ, where A is final amount, P is principal, r is interest rate, and n is number of periods

Example: For continuous compound interest, the formula A = Pe^(rt) is used, where e is Euler's number

Highlight: The half-life formula N(t) = N₀(1/2)^(t/t₁/₂) is crucial in radioactive decay calculations

Vocabulary: Asymptotes are lines that a curve approaches but never touches, defined by x = h and y = k in hyperbolic functions

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

Page 4: Trigonometric Functions and Probability

This page explores trigonometric relationships and probability calculations, including the laws of sines and cosines.

Definition: The law of cosines states that a² = b² + c² - 2bc cos(A) for any triangle

Example: The area of any triangle can be calculated using A = de sin(f), where d and e are sides and f is the included angle

Highlight: Permutations (P(n,r) = n!/(n-r)!) calculate arrangements where order matters

Vocabulary: The law of sines relates side lengths to angles: sin(A)/a = sin(B)/b = sin(C)/c

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

Page 5: Advanced Mathematical Concepts

This page concludes with advanced mathematical concepts and specialized formulas for probability and trigonometric calculations.

Definition: The probability formula for multiple selections involves combinations and specific conditions

Example: Vertical shifts in trigonometric functions are represented by adding or subtracting constants

Highlight: The tangent function V = tan(θ) relates to the ratio of sine and cosine

Vocabulary: Probability calculations often involve combinations (C(n,r) = n!/(r!(n-r)!)) for selecting items where order doesn't matter

quadratic formula: x = -b+√b²-4ac 2a to find axis of symmetry: b 2a to find vertex of quadratic in x intercept form p+q 2 slope intercept y

Page 1: Essential Algebraic Formulas

This page introduces fundamental algebraic equations and formulas essential for mathematical problem-solving. The content focuses on various forms of linear and quadratic equations.

Definition: The quadratic formula is used to find the roots of any quadratic equation: x = (-b ± √(b² - 4ac))/2a

Example: To find the axis of symmetry of a parabola, use the formula -b/2a

Highlight: The vertex form of a quadratic equation, f(x) = a(bx – h) + k, is particularly useful for graphing parabolas and finding maximum/minimum points

Vocabulary: Slope-intercept form (y = mx + b) represents a linear equation where 'm' is the slope and 'b' is the y-intercept

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Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying