Mini-Lecture 6.7: Quadratic Equations and Problem Solving | Lecture Note - Edubirdie

University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
Views:

305

Pages:

1
Author:

Marin Mason

Mini-Lecture 6.7 Quadratic Equations and Problem Solving Learning Objectives: 1. Solve problems that can be modeled by quadratic equations. Examples: 1. Represent each given condition using a single variable, x. a) The length and width of a rectangle whose width is half the measurement of the length. b) Two consecutive integers. c) The base and height of a triangle whose height is 3 less than 5 times its base. 2. Use the information given to solve the following problems. a) The area of a square is 144 ft2. Find the length of its side. b) The area of the circle is 81π square inches. Find the radius. c) The sum of two numbers is 16. The sum of their squares is 130. Find the numbers. d) A roofer drops a hammer from the top of a 64-foot roof. The height of the hammer after t seconds is given by h = −16t 2 + 64 . When will the hammer hit the ground? e) The hypotenuse of a right triangle is 6 inches more than the shorter leg. The longer leg is 3 inches more than the shorter leg. Find the lengths of all three sides. Teaching Notes: • • • • Many students struggle with word problems. Most students have trouble with converting the words to mathematical expressions. Refer students to Chapter 2, Section 2.4, General Strategy for Problem Solving. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) x=length, 1/2x = width; 1b) x, x+1; 1c) b=x, h=5x-3; 2a) 12 ft.; 2b) 9 in.; 2c) 7, 9; 2d) after 2 seconds; 2e) 9, 12, 15

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