Quadratic Equations Can Have Two, One, or No Solutions
Quadratic equations with one variable can have one solution, two solutions, or no solution at all.
Practical Problem: Phone Calls With a Surcharge
Using the slope-intercept form of equation, the amount of a hotel will charge to make a call from the phone in their room is calculated.
Practical Problem: The Cost of Plumbing Repairs
A practical application of the slope-intercept equation involving rate of change is demonstrated.
Practical Problem: Find the Rate of Gas Pumped
Illustrating the slope formula with a practical rate problem.
Practical Problem: Length of the Longest Object
The Pythagorean Theorem is used to calculate the length of the longest item that will fit into a suitcase.
Practical Problem: How Much Land to Buy
A practical problem involving the purchase of land is presented. The available information is organized into a table, an equation is written, then solved using the least common denominator to get a quadratic equation, and the solution checked.
Practical Problem: Homes and Apartments on 100 Acres
Calculating the number of houses and apartments that can be built on a 60-acre parcel of land given the amount of land allowed for each living unit is expressed in a system of equations involving fractions and solved using the least common denominat...
Practical Problem: How Long it Will Take to do Payroll
A work problem requires finding out how long it will take two workers with different work speeds to complete a task. The process of developing an equation and solving it are detailed.
Practical Problem: Ingredients for Small and Large Pizzas
Solve a practical problem involving making pizzas, given the ingredients available to use and how much of each ingredient is used for each pizza. The solution is demonstrated using both the elimination and the substitution methods.
Solving a Word Problem Using Two Variables
Writing and solving a word problem using a two-variable approach.