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 Your Notes VOCABULARY Quadratic formula A formula that gives the solutions of any quadratic equation in standard form THE QUADRATIC FORMULA The roots of the polynomial and the solutions of the quadratic equation are when a ≠ 0 and Example 1 Multiple Choice Practice Which is one of the solutions to the equation  Solution Quadratic formula Substitute values in the quadratic formula: a = 2 , b = -3 , and c = -5 . Simplify. Simplify the square root. One solution is -1. The correct answer is B Your Notes Example 2 Use the quadratic formula Crabbing A crabbing net is thrown from a bridge, which is 35 feet above the water. If the net's initial velocity is 10 feet per second, how long will it take the net to hit the water? Solution The net's initial velocity is v = 10 feet per second and the net's initial height is s = 35 feet. The net will hit the water when the height is 0 feet. Vertical motion model Substitute for h, v, and s. Substitute values in the quadratic formula: a = -16 , b= 10 , and c = 35 . Simplify. The solutions are and Because time cannot be a negative number, disregard the negative solution. So, the net will hit the water in about 1.82 seconds. Guided Practice Complete the following exercises. 1. Use the quadratic formula to solve  and 2. In Example 2, suppose the net was thrown with an initial velocity of 5 feet per second from a height of 20 feet. How long would it take the net to hit the water? about 1.29 seconds Your Notes METHODS FOR SOLVING QUADRATIC EQUATIONS Methods When to Use Factoring Use when a quadratic equation can be factored easily. Graphing Use when approximate solutions are adequate. Finding Use when solving an equation that can square roots be written in the form x2 = d . Completing Can be used for any quadratic equation the square Can be used for any quadratic equation the square but is simplest to apply when a = 1 and b is an even number. Quadratic Can be used for any quadratic equation. formula Example 3 Choose a solution method Tell what method(s) you would use to solve the quadratic equation. Explain your choice(s). Solution a. The quadratic equation cannot be factored easily and completing the square would result in many fractions . So, the equation can be solved using the quadratic formula . b. The quadratic equation can be solved using square roots because the equation can be written in the form x2 = d. Guided Practice Complete the following exercise. Homework 3. Tell what method(s) you would use to solve . Explain your choices(s). factoring: the expression can be factored easily; completing the square: the equation is of the form where a= 1 and b is an even number.