Solving Quadratic Word Problems

This video tutorial provides a brief lesson on solving quadratic word problems. It begins with an introduction to the types of problems that can be solved using quadratic equations and outlines the steps required to solve them. The tutorial includes two examples: one involving the expansion of a rectangular deck and another about adding a walkway around a swimming pool. Each example demonstrates how to set up and solve the quadratic equations, emphasizing the use of the quadratic formula and factoring techniques.

What is the first step in solving quadratic word problems?

• Set up the quadratic equation

• Read the problem and underline important information

• Draw a diagram

• Solve the equation

What should you do if the problem involves a physical shape?

• Draw a diagram if necessary

• Immediately solve the equation

• Guess the dimensions

• Ignore the shape

In the deck size problem, what is the original size of the deck?

• 10 feet by 20 feet

• 20 feet by 15 feet

• 15 feet by 20 feet

• 15 feet by 25 feet

What is the maximum area allowed for the deck after expansion?

• 1000 square feet

• 850 square feet

• 900 square feet

• 800 square feet

Which method is suggested for solving the deck expansion problem?

• Factoring

• Graphing

• Quadratic formula

• Completing the square

What is the correct equation setup for the new length and width of the deck?

• (15 + x)(20 + x) = 900

• (20 + x)(15 + x) = 800

• (15 + x)(20 + x) = 1000

• (20 + x)(15 + x) = 900

What is the width of the walkway to be added around the pool?

• 1.5 meters

• 2 meters

• 0.5 meters

• 1 meter

How is the equation for the area of the pool and walkway set up?

• (12 + 2x)(20 + 2x) = 308

• (20 + x)(12 + x) = 308

• (12 + x)(20 + x) = 308

• (20 + 2x)(12 + 2x) = 308

What is the correct factorization of the equation derived from the pool and walkway problem?

• 4(x^2 + 16x - 17) = 0

• 4(x^2 + 17x - 16) = 0

• 4(x^2 + 8x - 34) = 0

• (x^2 + 16x - 17) = 0

Which of the following is a correct step in solving quadratic equations?

• Always multiply the highest degree terms

• Set all terms to zero before factoring

• Use only the quadratic formula

• Ignore negative solutions if dealing with physical dimensions