Quadratic Equations Video 1
Explaining the standard form for a quadratic equation and the possible number of solutions
Problem: Solve the following equation: \(2x^2-7x-4=0\)
Explaining the standard form for a quadratic equation and the possible number of solutions
Solving quadratic equations with the difference of two squares formula
Solving quadratic equations by factoring
Solving a quadratic equation by factoring
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Solving an equation with exponential functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving a trigonometric equation by factoring
Solving a trigonometric equation
Finding the domain of a function with a natural logarithm and denominator
Explaining when a quadratic equation does not have a real solution
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions
Finding the difference quotient for a quadratic function
Factoring a quadratic
Factoring a polynomial
Factoring a quadratic
Dividing rational expressions and simplifying
Subtracting rational expressions and simplifying
Performing operations with rational expressions and simplifying
Performing operations with rational expressions and simplifying
Solving an equation using the quadratic formula
Solving a quadratic equation by completing the square
Solving a polynomial equation using factoring by grouping
Solving a rational equation and checking the solutions
Solving a quadratic equation using the quadratic formula
Finding the x-intercepts of quadratic functions
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving an equation with exponential functions by factoring
Finding the domain of a rational function using factoring
Explaining the graph and properties for the parent function of quadratics
Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
Explaining how to solve radical equations and then solving example problems
Solving equations with even roots and checking the solutions
Solving equations with odd radicals
Solving equations with multiple radicals
Explaining how to solve equations with power and exponential terms
Solving equations with exponential terms
Solving equations with base e exponential terms
Explaining how to solve logarithmic equations
Solving logarithmic equations with a single logarithm term
Solving logarithmic equations with multiple logarithm terms
Solving logarithmic equations with multiple logarithm terms on both sides
Solving equations that contain rational expressions
How to simplify rational expressions
Finding the maximum revenue, maximum profit, and break even quantity for given revenue and cost functions
Identifying quadratic functions and their properties
Finding the piecewise-defined function for a given graph along with its domain and range
Graphing a piecewise function
Solving an equation with exponential functions
Identifying the parent function and transformations for a given graph
Subtracting rational functions and then simplifying the result
Multiplying two rational functions and simplifying the result
Dividing rational functions and simplifying the result
Dividing and subtraction rational functions and simplifying the result
Explaining the Intermediate Value Theorem and the Bisection Method
Using the Intermediate Value Theorem and Bisection Method to approximate the solution of an equation
Factoring an algebraic expression
Determining if an equation represents a function
Putting a quadratic function in standard form and determining its properties
Putting a quadratic function in standard form and determining its properties
Putting a quadratic function in standard form and determining its properties
Finding the end behavior of a polynomial
Finding properties of a polynomial including zeros and end behavior
Finding properties of a polynomial including zeros and end behavior
Finding properties of a polynomial including zeros and end behavior
Using properties of a polynomial to find its graph
Solving a nonlinear inequality
Solving an equation with an exponential function
Solving an equation with an exponential function
Solving an equation with an exponential function
Solving an equation with an exponential function
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Modeling a population size with an exponential function
Solving a trigonometric equation
Solving a trigonometric equation
Solving a trigonometric equation
Solving a trigonometric equation
Solving a trigonometric equation
Using a double angle formula to solve a trigonometric equation
Using a double angle formula to solve a trigonometric equation
Using a double angle formula to solve a trigonometric equation
Using double angle formulas to evaluate trigonometric functions
Review of limits, continuity, and the Intermediate Value Theorem
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Continuity of Functions and the Intermediate Value Theorem
Review of the limit definition of a derivative and calculating the derivative
Differentials, linear approximations and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Review of work and average value
Examples finding the area bounded by curves
Examples finding a volume using disks, washers, and by slicing
Using the disk, washer, and shell method to find a volume of revolution
Finding volume using using disks, washers and the shell method
Using integrals to solve work problems and find the average value
Finding the length of a curve given by parametric equations
Explaining all four cases of partial fraction decomposition
Proving associative and scalar multiplication properties for vectors
Review of limits, continuity, and the Intermediate Value Theorem
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Continuity of Functions and the Intermediate Value Theorem
Review of the limit definition of a derivative and calculating the derivative
Differentials, linear approximations, and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Using the Chain Rule to prove facts about derivatives
Review of work and average value
Examples finding the area bounded by curves
Examples finding a volume using disks, washers, and by slicing
Using the disk, washer, and shell method to find a volume of revolution
Finding volume using using disks, washers and the shell method
Using integrals to solve work problems and find the average value
Using integrals to solve work problems and find the average value
Finding the limit of a three-dimensional vector function
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
Finding the domain of a function with a denominator, square root, and logarithm
Explaining domain restrictions for denominators, even roots, and logarithms
Finding the domain of a function with a square root in the denominator
Finding the domain of a function with a root and a logarithm in the denominator
Finding the domain of a logarithmic function
Finding the domain of even and odd roots
Finding the domain of functions with even and odd roots
Finding the domain of several rational functions
Finding the domain of a rational function
Explaining how to find any holes and vertical asymptotes of a rational function
Explaining the main three forms for linear equations
Discussing properties of linear functions
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Discussing how to write the equation of a line through two given points
Writing a linear equation of profit from a business word problem
Solving a linear equation algebraically and showing how this relates to the graph
Solving a linear equation algebraically
Solving a linear equation algebraically and showing how this relates to the graph
Explaining the format and possible solutions for a system of two linear equations
Solving a system of linear equations with two variables
Solving a system of two linear equations with two variables using the elimination method
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Explaining the general properties of even and odd root functions
How to rewrite radical terms as power terms
Properties of exponents applied to power and exponential expressions
Properties of multiplying and simplifying power and exponential expressions
Properties of exponents applied to power and exponential expressions
Properties of exponential growth and decay functions
Properties of the exponential function with base e
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Simplifying an expression with both power and exponential functions using properties of exponents
Explaining the terminology and rules of logarithms
Explaining the basic properties of logarithmic functions
Expanding logarithmic expressions using logarithm rules
Condensing a logarithmic expression into a single logarithm
Adding and subtracting rational expressions by finding a common denominator
Explaining how to multiply and divide rational expressions
Performing algebraic operations with rational expressions and simplifying the answer
Discussing parent functions of rational functions and their properties
Finding horizontal asymptotes for rational functions
Explaining how to do polynomial long division
Finding horizontal asymptotes for rational functions
Determining the end behavior and horizontal asymptotes for rational functions
Explaining basic algebraic operations for fractions
Explaining all four cases of partial fraction decomposition
Explaining the format and possible solutions for a system of two linear equations