# Math 30-1 Help & Practice

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##### 1Factoring Polynomials

##### 2Quadratic Functions

- 2.1Introduction to quadratic functions
- 2.2Transformations of quadratic functions
- 2.3Quadratic function in general form:
*y = ax^2 + bx + c* - 2.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 2.5Completing the square
- 2.6Converting from general to vertex form by completing the square
- 2.7Shortcut: Vertex formula
- 2.8Graphing quadratic functions: General form VS. Vertex form
- 2.9Finding the quadratic functions for given parabolas
- 2.10Applications of quadratic functions

- 2.1Introduction to quadratic functions
##### 3Functions

##### 4Transformations of Functions

- 4.1Transformations of functions: Horizontal translations
- 4.2Transformations of functions: Vertical translations
- 4.3Reflection across the y-axis:
*y = f(-x)* - 4.4Reflection across the x-axis:
*y = -f(x)* - 4.5Transformations of functions: Horizontal stretches
- 4.6Transformations of functions: Vertical stretches
- 4.7Combining transformations of functions

- 4.1Transformations of functions: Horizontal translations
##### 5Polynomial Functions

- 5.1What is a polynomial function?
- 5.2Polynomial long division
- 5.3Polynomial synthetic division
- 5.4Remainder theorem
- 5.5Factor theorem
- 5.6Rational zero theorem
- 5.7Characteristics of polynomial graphs
- 5.8Multiplicities of polynomials
- 5.9Imaginary zeros of polynomials
- 5.10Determining the equation of a polynomial function
- 5.11Applications of polynomial functions
- 5.12Solving polynomial inequalities
- 5.13Fundamental theorem of algebra
- 5.14Descartes' rule of signs

- 5.1What is a polynomial function?
##### 6Radical Functions

##### 7Rational Functions

##### 8Exponential Functions

- 8.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 8.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 8.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 8.4Exponents: Negative exponents
- 8.5Exponents: Zero exponent:
*a^0 = 1* - 8.6Exponents: Rational exponents
- 8.7Solving exponential equations using exponent rules
- 8.8Graphing exponential functions
- 8.9Graphing transformations of exponential functions
- 8.10Finding an exponential function given its graph

- 8.1Exponents: Product rule
##### 9Logarithmic Functions

- 9.1What is a logarithm?
- 9.2Converting from logarithmic form to exponential form
- 9.3Evaluating logarithms without a calculator
- 9.4Common logarithms
- 9.5Natural log: ln
- 9.6Evaluating logarithms using change-of-base formula
- 9.7Converting from exponential form to logarithmic form
- 9.8Solving exponential equations with logarithms
- 9.9Product rule of logarithms
- 9.10Quotient rule of logarithms
- 9.11Combining product rule and quotient rule in logarithms
- 9.12Evaluating logarithms using logarithm rules
- 9.13Solving logarithmic equations
- 9.14Graphing logarithmic functions
- 9.15Finding a logarithmic function given its graph

- 9.1What is a logarithm?
##### 10Applications of Exponential and Logarithmic Functions

- 10.1Exponential growth and decay by a factor
- 10.2Exponential decay: Half-life
- 10.3Exponential growth and decay by percentage
- 10.4Finance: Compound interest
- 10.5Continuous growth and decay
- 10.6Logarithmic scale: Richter scale (earthquake)
- 10.7Logarithmic scale: pH scale
- 10.8Logarithmic scale: dB scale
- 10.9Finance: Future value and present value

- 10.1Exponential growth and decay by a factor
##### 11Trigonometric Ratios and Angle Measure

- 11.1Angle in standard position
- 11.2Coterminal angles
- 11.3Reference angle
- 11.4Find the exact value of trigonometric ratios
- 11.5ASTC rule in trigonometry (
**A**ll**S**tudents**T**ake**C**alculus) - 11.6Unit circle
- 11.7Converting between degrees and radians
- 11.8Trigonometric ratios of angles in radians
- 11.9Radian measure and arc length

- 11.1Angle in standard position
##### 12Graphing Trigonometric Functions

##### 13Applications of Trigonometric Functions

##### 14Trigonometric Identities

##### 15Solving Trigonometric Equations

- 15.1Solving first degree trigonometric equations
- 15.2Determining non-permissible values for trig expressions
- 15.3Solving second degree trigonometric equations
- 15.4Solving trigonometric equations involving multiple angles
- 15.5Solving trigonometric equations using pythagorean identities
- 15.6Solving trigonometric equations using sum and difference identities
- 15.7Solving trigonometric equations using double-angle identities

- 15.1Solving first degree trigonometric equations
##### 16Permutations and Combinations