7.4 The Quadratic Formula BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Thus far, we have solved quadratic equations by factoring and the method of completing the square Property. We have one more method to learn; it is the Quadratic Formula. The method can be used whenever the quadratic equation is not factorable. This formula is as follows: The Quadratic Formula Before we get started, let’s practice simplifying some rational expressions Divide all terms by 6 Factor out 2 from numerator then reduce Divide all terms by 2 or shortcut: No common factor.

7.4 The Quadratic Formula BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 The first step is to identify a, b, and c by comparing to the standard form ax 2 + bx + c = 0. Then, replace these numbers into the quadratic formula and simplify. Hint: since you need to memorize the formula, it is always a good idea to just write it down whenever you need to use it. The more times you write something down, it will help you to memorize whatever it is you need to memorize. 2. Substitute a, b, and c into the Q.F. 3. Simplify 1. Write down the Q.F. and a, b and c. Your Turn Problem #3

7.4 The Quadratic Formula BobsMathClass.Com Copyright © 2010 All Rights Reserved Substitute a, b, and c into the Q.F. 3. Simplify 1. Write down the Q.F. and a, b and c. Solution: Your Turn Problem #4

7.4 The Quadratic Formula BobsMathClass.Com Copyright © 2010 All Rights Reserved Substitute a, b, and c into the Q.F. and simplify. 2. Now we can write down the Q.F. and a, b and c. Solution: 1. Since this equation is not written in standard form, that will be our first step. Distribute on the LHS, then get a zero on the RHS. Note: Since the solutions are rational numbers, the quadratic equation was actually factorable. Your Turn Problem #4

7.4 The Quadratic Formula BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 Solution: 2. Substitute a, b, and c into the Q.F. 3. Simplify 1. Write down the Q.F. and a, b and c. Whenever we have a complex number, it must be written in a+bi form. Your Turn Problem #5

7.4 The Quadratic Formula BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 In past equations, we would check our answer to verify the solution was correct. However it can be extremely difficult to do this. Fortunately, we have an alternative method for verifying the solutions. We have the following two relationships: The Sum and Product Check. The sum of the roots =The product of the roots =, 1 st, find the sum of the roots. 2 nd, find the product of the roots. Since these values match, our answers are correct. (We solved this example earlier in this lesson.) Example 6. Check the solution to the quadratic equation using the sum and product check. Your Turn Problem #6 Check the solution to the quadratic equation using the sum and product check. The End. B.R