Success Center Directed Learning Activity (DLA) Quadratic Formula M109.1

Success Center Directed Learning Activity (DLA) Quadratic Formula M109.1

Directed Learning Activity Quadratic Formula Description: In this Directed Learning Activity (DLA), you will learn about the Quadratic formula. Prior Knowledge: In order to complete this DLA, you will need to know how to simplify a radical. Simplify: a) 60 b) 5 5 5 6 10 60 180 90 45 5 9 5 (6) 4(1)() 6 4(1)() 6 1 4 6 Materials: A scientific calculator may be needed. Directions: Please read the examples and answer the questions that follow carefully and in order. Please do not skip ahead. If you have a question, please ask for help. After reading the examples in the gray boxes, spend some time thinking about what is being presented. After you feel you understand the examples, try to answer the practice questions. When you are finished, review the DLA with a tutor or an instructor. Don t worry: You are not being graded. This is a learning activity, and you are not expected to know everything. Part One: Introducing the Quadratic Formula The quadratic formula is used to solve a quadratic equation. After the quadratic is placed in descending order and set equal to zero, the letters a, b, and c are assigned for the values of the coefficients and the constant. Each letter in the formula is then replaced with a parenthesis, and the values are substituted into the parentheses. We will go over how to simplify the problem in the following pages. bx c 0 a = x b b 4ac a x 5x 0 b = 5 c = Here is a story to help you remember the formula: The negative boy Couldn t decide Whether to go to the radical party, Where the square bouncer Removed 4 alcoholic cans, And it was all over at am. ( 5) x ( 5) () 4()(), 1 And here is a song (as sung on YouTube): To the tune of Pop Goes the Weasel : Negative b plus or minus the square root of b squared minus four ac all over two a.

Part Two: Simplifying the Quadratic Formula Example 1: Solve for x. x 5x 0 1 ( 5) 5 4()() 5 4 1 bx c 0 x 5x 0 4()() b x ( 5) x b 4ac a ( 5) () 4()() Using order of operations, we start with groupings. The radical is our first grouping. We want to simplify the radical first. The radical is the most complicated part of the problem, and, once it is simplified, the problem should become less complicated. Once we have simplified the radical, we can continue to simplify the problem. The numerator and denominator are simplified separately. ( 5) 1 5 1 5 1 5 1 6 4 x x,, x, 1 () 4 4 4 4 4 Example : Solve for x. x 7x 8 0 6 (6) 6 4()( 1) 6 180 5 bx c 4()( 1) 144 0 x 6x 1 0 b x (6) x b 4ac a (6) () 4()( 1) Follow the same steps described in Example 1: Using order of operations, we start with groupings. The radical is our first grouping. We want to simplify the radical first. The radical is the most complicated part of the problem, and, once it is simplified, the problem should become less complicated. Once we have simplified the radical, we can continue to simplify the problem. (6) 6 5 6 6 5 6 6 5 x 1 5 x 1 5, 1 5 () 6 6 6

Practice: = b) = Answers: a) x=4, -8/5 b) = Part Three: Setting the Equation to Zero First Example : Solve k 6k The formula requires the equation to be set equal to zero. k 6 48 4 bx c 0 In this example, subtracting three from both sides will give us an equation that is equal to zero. k 6k k k 6k 6k 0 bx c 6k 1 b b 4ac 0 x a k is the same as 1k, so a=1 ( 6) ( 6) 4(1)( ) 0 x (1) Remember to start by simplifying the radical separately. ( 6) 4(1)( ) 6 4(1)( ) ( 6) 4 x (1) 6 4 6 4

Practice 0 y y b) 5x x 1 7 4xx Answers: a) x=/5, -1/4 b) = Part Four: Reflection a) Name one thing that you understand better about the quadratic formula as a result of completing this activity. b) Name one thing that you still do not understand about the quadratic formula. c) Can you think of a way to apply the quadratic formula to the work in a course you are currently taking? STOP. Please go over your work with a tutor at this time.

M109.1 Quadratic Formula PRINT STUDENT NAME STUDENT # Tutor Feedback: The student completed the entire activity. The student attempted to answer every question. The student demonstrated an understanding of the process of using the quadratic formula to solve quadratic equations during the discussion of his/her work. Additional Comments: PRINT INSTRUCTOR/TUTOR NAME DATE INSTRUCTOR/TUTOR SIGNATURE STUDENT DO NOT FORGET TO TURN THIS SHEET IN AT THE FRONT DESK! You may not get credit for completing this DLA if you fail to leave this sheet with the front desk receptionist.