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Quadratic Formula Quiz

Bestselling Learn Guitar on Android! Math instructor and Mahalo Math Channel host Allison Moffett helps explain the quadratic formula through a series of quizzes. Here she tests you on your knowledge of the satisfying conditions of the quadratic formula and the practical use of the discriminant in arriving at its solutions. In mathematics, a quadratic equation is one in which the variable gets squared. graph of a quadratic equation is a parabola, and its solutions are the points where it crosses the axis. One way to solve a quadratic equation is by using the quadratic formula. quadratic formula states that x = (-b ± √(b2-4ac))/2a, where a cannot equal 0. In order to satisfy the conditions for use of the quadratic formula, you must have a quadratic equation in this form: ax^2 + bx + c = 0. this equation, the letters a, b, and c are the coefficients that are later used in the quadratic formula. In the quadratic formula, the b^2 - 4ac term is called the discriminant because it can discriminate between the possible types of solutions to your equation. b^2 - 4ac is positive, you will arrive at two real solutions. If it is negative, you get two complex solutions. And if it is 0, you get one solution. Step 1: Determine If Satisfying Conditions Are Met --------------------------------------------------------------------- Mahalo math instructor Allison Moffett poses the question of whether or not the equation 4x^2 = 9 is in the correct form to use the quadratic formula. It is not. While it does have the necessary x^2 term for a quadratic equation, to satisfy the condition for the quadratic formula all terms of the equation must be on one side with the equation set to equal 0. Step 2: Use Algebra to Make Equation Satisfy the Condition --------------------------------------------------------------------- In order to make the equation satisfy the condition for use of the quadratic formula, you will need to get all the terms to one side and set the equation to zero. accomplish this, you must subtract 9 from each side. This would create the equation 4x^2 - 9 = 9 - 9, which you may simplify to 4x^2 - 9 = 0. Now your equation is in a form that satisfies the condition. Step 3: Plug Coefficients Into Quadratic Formula --------------------------------------------------------------------- What are the values of the coefficients a, b, and c in the equation 4x^2 - 9 = 0? If our equation must be in the form ax^2 + bx + c = 0, then a must be 4 and c must be -9. As there is no x term, b must be 0. So, according to the quadratic formula: x = (0 ± √(0 - (4 x 4 x -9))) / 2(4).? Step 4: Use Discriminant to Deduce Type of Solutions --------------------------------------------------------------------- Allison next asks what the discriminant can tell us about the equation's solutions. The discriminant in this situation is 0 - (4 x 4 x -9). equals - (-144), which is the same as 144, a positive number. As it is a positive number, there will be two real solutions. ? Read more by visiting our page at:
Length: 00:46


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