Mini-Lecture 9.3: Solving Quadratic Equations by the Quadratic Formula

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

2023
Views:

203

Pages:

1
Author:

gydraddolmxla

Mini-Lecture 9.3 Solving Quadratic Equations by the Quadratic Formula Learning Objectives: 1. Use the quadratic formula to solve quadratic equations. 2. Approximate solutions to quadratic equations. 3. Determine the number of solutions of a quadratic equation by using the discriminant. Examples: 1. Identify the value of a, b, and c in each quadratic equation. a) 2 x 2 − 7 x − 9 = 0 b) 4 x 2 − 3 x − 7 = 0 c) x 2 − 15 = 0 Use the quadratic formula to solve each quadratic equation. d) x 2 + 7 x + 10 = 0 e) 3 p 2 − 23 p + 14 = 0 f) 2 x 2 − 7 x − 4 = 0 g) x 2 + 5 x − 8 = 0 h) x 2 − 7 = 0 i) x 2 − 3 x + 4 = −5 2. Use the quadratic formula to solve each quadratic equation. Find the exact solutions; then approximate these solutions to the nearest tenth. a) 4 y 2 + 2 y − 3 = 0 b) 2 x 2 + 4 x = −1 c) 1 2 1 1 x − x= 8 4 2 3. Use the discriminant to determine the number of solutions of each quadratic equations. a) x 2 − 5 x + 4 = 0 b) 2 x 2 − 3x + 5 = 0 c) x 2 − 12 x + 36 = 0 Teaching Notes: • • • • • Most students have difficulty learning the quadratic formula. Suggest that they put the formula to the tune of “Pop Goes The Weasel”. “x equals negative b plus or minus square root, b squared minus 4ac all over 2a”. Most students make careless errors upon evaluation. Encourage students to clearly write the values for a, b, and c before substitution. Remind students that the fraction bar is under the entire numerator −b ± b 2 − 4ac . Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) a=2, b=-7, c=-9; 1b) a=4, b=-3, c=-7; 1c) a=1, b=0, c=-15; 1d) -2, -5 ; 1e) 7, 2/3; 1f) 4, -1/2 −5 ± 57 −1 ± 13 −2 ± 2 ; 1h) ± 7 ; 1i) not a real number; 2a) , 0.7, -1.2; 2b) , -0.3, -1.7; 2 4 2 2c) 1 ± 5 , 3.2, -1.2; 3a) two distinct real solutions; 3b) no real solutions; 3c) one real solution 1g)