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Updated Feb 25, 2026

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5 pages

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

Shreeya Ram

@shreeyaram_iuea

A comprehensive guide to essential mathematical formulas and concepts, focusing... Show more

1 / 5

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

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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Algebra 2

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229

•

Updated Feb 25, 2026

•

5 pages

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

Shreeya Ram

@shreeyaram_iuea

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 examplesand... Show more

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

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Access to all documents

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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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

Sign up to see the contentIt's free!

Access to all documents

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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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

Sign up to see the contentIt's free!

Access to all documents

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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

$Formulas quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2\alpha}$ to find axis of symmetry: $-\frac{b}{2a}$ to find vertex of quadr$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

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