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

2023
Views:

344

Pages:

1
Author:

domdairech8y

Mini-Lecture 9.1 Solving Quadratic Equations by the Square Root Property Learning Objectives: 1. Use the square root property to solve quadratic equations. 2. Solve problems modeled by quadratic by quadratic equations. Examples: 1. Solve each equation by factoring. a) x 2 − 36 = 0 b) 5 x 2 − 125 = 0 c) x 2 − 4 x = 21 d) 2 x 2 = x + 10 Use the square root property to solve each quadratic equation. e) x 2 = 49 i) ( x − 4 ) = 25 2 f) x 2 − 33 = 0 g) x 2 + 100 = 0 2 1⎞ 1 ⎛ j) ⎜ x − ⎟ = 5⎠ 25 ⎝ k) ( 2 x − 1)2 = 49 h) 25 x 2 = 8 l) ( a + 2 )2 = 15 2. Solve the following applications. Round each answer to the nearest tenth of a second. a) Use the formula h = 16t 2 to solve the following: determine the time of a stuntman’s fall if he jumped from a height of 450 feet. b) Use the formula for the area of a square A = s 2 where s is the length of a side. If the area of a square is 40 square inches, find the length of the side. c) Use the formula for the area of a square A = s 2 where s is the length of a side. If the area of the square base of a monument is 2200 square feet, find the length of the side. Teaching Notes: • • • • • Many students will need a review of factoring, especially factoring difference of two squares. Many students need extra practice working with the “+ “ symbol. Some students need to always write their answers by separating the “+” symbol, and writing the positive solution and negative solution. Remind students with applications that the negative solution will be an extraneous solution. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) ±6 ; 1b) ±5 ; 1c) -3, 7; 1d) -2, 1i) -1, 9; 1j) 0, 5 2 2 ; 1e) ±7 ; 1f) ± 33 ; 1g) not real; 1h) ± ; 2 5 2 ; 1k) -3, 4; 1l) −2 ± 15 ; 2a) 5.3 s; 2b) 6.3 in.; 2c) 46.9 ft. 5