Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name: Date: Page 1 of 5 Activity 2.2.6 Deriving the Quadratic Formula Directions: In Column 1, you are given precise instructions on the steps you need to take in order to “complete the square” to solve the quadratic equation below. In Column 2, show the manipulation you are making to the quadratic equation using numbers. In Column 3, show the exact same manipulation you perform in Column 2, but to a quadratic equation in standard form with the variables a, b, and c. Solve the quadratic equation 5x 2 + 6x - 2 = 0 . Column 1: Steps to Complete the Square Step 1: Isolate the x terms by using the Addition Property of Equality. Column 2: Show with Numbers for 5x 2 + 6x - 2 = 0 Column 3: Show with Variables for ax 2 + bx + c = 0 Step 2: Change the coefficient of the quadratic term to 1 by dividing both sides of the equation by the coefficient of the quadratic term. Step 3: Divide the coefficient of the linear term in half and square it. Add the result to both sides of the equation using the Addition Property of Equality. This creates a perfect square trinomial, which can be factored into the square of a binomial. Activity 2.2.6 Connecticut Core Algebra 2 Curriculum Version 3.0 Name: Date: Page 2 of 5 Step 4: Factor the perfect square trinomial you just created into the square of a binomial. Find a common denominator to add together the rational expressions. Take the square root of both sides of the equation and simplify. Solve for x and simplify the expression. Assume a > 0. You have just derived the quadratic formula!!! Activity 2.2.6 Connecticut Core Algebra 2 Curriculum Version 3.0 Name: Date: Page 3 of 5 NOTE: A quadratic equation in standard form is expressed as ax 2 + bx + c = 0 . For the given quadratic equation a = 5, b = 6 and c = -2 . Substitute these values into the quadratic formula and simplify your result below. Does your result match the result in the last box of column two? Applying the Quadratic Formula x= -b ± b2 - 4ac 2a Directions: Now that you have derived the quadratic formula, use it to solve the following quadratic equations below. First, identify the coefficients a, b, and c in the spaces given. Then substitute those values into the quadratic formula and simplify the expression. 1. x 2 +10x + 25 = 0 a = ______ b = ______ c = ______ Activity 2.2.6 2. x 2 - 4x + 4 = 0 a = ______ b = ______ c = ______ Connecticut Core Algebra 2 Curriculum Version 3.0 Name: 3. Date: x2 - x - 6 = 0 a = ______ b = ______ c = ______ 5. 6x 2 +11x + 3 = 0 a = ______ b = ______ c = ______ 7. 2x 2 + 8x + 3 = 0 a = ______ b = ______ c = ______ Activity 2.2.6 Page 4 of 5 4. x 2 - 2x - 35 = 0 a = ______ b = ______ c = ______ 6. 5x 2 - 21x + 4 = 0 a = ______ b = ______ c = ______ 8. 3x 2 - 6x -10 = 0 a = ______ b = ______ c = ______ Connecticut Core Algebra 2 Curriculum Version 3.0 Name: Date: Page 5 of 5 Recall that the square root of a negative number in not a Real Number. Therefore, if your quadratic formula results with a negative number inside the square root symbol, then the answer is “no Real Number solution”. Some of the following equations have a real number solution, and some do not: 9. 2 x 2 x 3 0 10. a = ______ b = ______ c = ______ 11. x 2 9 0 a = ______ b = ______ c = ______ 2x2 x 3 0 a = ______ b = ______ c = ______ 12. x2 9 0 a = ______ b = ______ c = ______ 13. 5 x 2 8 x 5 0 a = ______ b = ______ c = ______ Activity 2.2.6 Connecticut Core Algebra 2 Curriculum Version 3.0