Solving an Inequality with a Polynomial
Solving an inequality with a polynomial by factoring and using a sign diagram
Problem: Solve the following inequality:\[-9x^2 + 100 \geq 0\]
Solving an inequality with a polynomial by factoring and using a sign diagram
Solving an inequality with a rational expression by factoring and using a sign diagram
Solving an inequality with two rational expressions using a sign diagram
Solving an inequality with a rational expression using a sign diagram
Solving a nonlinear inequality
Solving a nonlinear inequality
Solving a nonlinear inequality
Factoring a quadratic where the leading coefficient is 1
Factoring quadratics where the leading coefficient is not 1
Factoring a sum of cubes and a difference of cubes
Factoring a quadratic polynomial
Factoring a quadratic function
Finding the domain of a function with a quadratic inside a square root
Solving an equation with exponential functions
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
Finding the x-intercepts of quadratic functions
Solving a nonlinear inequality
Solving a trigonometric equation by factoring
Solving a trigonometric equation
Finding all solutions to a trigonometric equation with sine
Solving a trigonometric equation with secant by factoring
Solving a trig equation with sine and cosine using aPythagorean Identity
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Solving an equation with logarithmic functions
Factoring several polynomials by grouping
Factoring a difference of two squares
Factoring a cubic polynomial by grouping
Finding the greatest common factor of a polynomial and then factoring it out
Simplifying a rational expression
Adding and then simplifying two rational expressions
Multiplying two rational expressions and then simplifying
Dividing rational expressions and then simplifying the answer
Adding two rational expressions and then simplifying the answer
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a rational function with its graph
Using the quadratic formula to find the roots of a function
Finding the roots of a cubic polynomial
Finding the roots of a square root function
Finding the composition of a rational function and a quadratic
Finding and simplifying the difference quotient for a quadratic function
Finding the absolute maximum or absolute minimum of a quadratic
Writing the standard form of quadratic function given its vertex and one other point
Solving an equation with exponential functions by factoring
Solving a equation with exponential functions by factoring
Solving an quadratic-like equation with sine by factoring
Finding the domain of a function with a natural logarithm and denominator
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 a quadratic equation by factoring
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Explaining how to graph linear inequalities
Graphing two linear inequalities
Sketching the solution set and finding the corner points for a system of linear inequalities
Graphing the solution set of an inequality with two variables
Graphing the solution set of an inequality with two variables
Graphing the solution set of system of linear inequalities
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
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
Determining the intervals where a function is increasing and decreasing
Factoring an algebraic expression
Solving a linear inequality and graphing the solution set
Solving a linear inequality and graphing the solution set
Solving an inequality with an absolute value and graph its solution set
Solving an inequality with an absolute value
Solving a quadratic equation using the quadratic formula
Solving an equation using the quadratic formula
Solving a quadratic equation by completing the square
Solving a polynomial equation using factoring by grouping
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 an equation with exponential functions by factoring
Differentials, linear approximations and quadratic approximations
Review of work and average value
Finding the length of a curve given by parametric equations
Explaining all four cases of partial fraction decomposition
Differentials, linear approximations and quadratic approximations
Using the Chain Rule to prove facts about derivatives
Review of work and average value
Using integrals to solve work problems and find the average value
Explaining all four cases of partial fraction decomposition
Finding the limit of a three-dimensional vector function
Explaining all four cases of partial fraction decomposition
Solving a trigonometric equation with tangent and sine by factoring
Solving a trigonometric equation with sine and cosine by factoring
Finding the coordinate vector of a quadratic given a basis for the vector space
Solving a rational equation and checking the solutions
Finding the properties of a quadratic function such as the vertex, axis of symmetry, intercepts, etc.
Writing the equation of a line passing through two points
Writing the equation of a line through two points in slope-intercept form
Writing the equation of a graphed line in standard form
Finding the roots of a function with an absolute value
Finding the domain of a rational function
Finding the domain of a rational function
Finding the domain of a function with a fraction and radicals
Finding the composition of two functions with exponentials and logarithms
Finding the composition of two functions with a square root and a fractional exponent
Finding the composition of two functions with a cube root and a fractional exponent
Finding the composition of two functions
Finding the inverse of a linear function and its domain
Finding the inverse of a square root function and its domain
Finding the inverse of a rational function and its domain
Finding the inverse of a rational function and its domain
Finding and simplifying the difference quotient for a rational function
Finding and simplifying the difference quotient for a square root function
Finding the component form and magnitude for a vector between two points
Performing calculations with vectors including addition, subtraction, and scalar multiplication
Calculating the dot product for three pairs of vectors
Finding a unit vector in the direction of a given vector
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations
Solving a system on two equations where one is linear and one is quadratic
Solving a equation with an exponential function
Solving an equation with two exponential functions with different bases
Finding the size of a population of rabbits with exponential growth
Finding the size of a population of rabbits with exponential decay
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Expanding a logarithmic expression using logarithm properties
Condensing logarithmic expressions into a single logarithm
Finding the exact value of logarithms using logarithmic properties
Finding the vertical asymptote of a logarithmic function
Finding the vertical asymptote of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Solving a logarithmic equation using properties of logarithms
Solving a logarithmic equation using properties of logarithms
Finding the values of all six trigonometric functions of an angle given a right triangle
Evaluating the other five trigonometric functions for an acute angle given the value of sine
Evaluating the other five trigonometric functions given sine and that tangent is negative
Finding the solutions to an equation with tangent in a given interval
Solving a trigonometric equation with sine and cosine on a given interval
Solving an equation with cosine on a given interval
Solving a trigonometric equation with sine on a given interval
Sketching one period of a transformed sine graph
Sketching one period of a cosine function with transformations
Finding the amplitude, period, phase shift, and vertical shift for a given sine function
Writing a cosine function for a given graph
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
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 when a quadratic equation does not have a real solution
How to simplify rational expressions
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions