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Transcript
MAC 1105 - Section 3.2b Solving Quadratic Equations Using the Quadratic Formula A. Skill Review 1. Simplify the following radical expressions a. 50 b. c. 3 72 200 d. 5 120 2. Simplify the following fractional expressions a. 6 12 5 3 b. 10 4 6 6 c. 14 2 3 7 d. 6 12 3 3. Use your calculator to calculate rounded decimal values for parts a and c of item 2 above. a. c. B. Quadratic Formula A Quadratic equation in the form ax2 + bx + c = 0 can be solved symbolically by substituting the values for a, b and c into the Quadratic Formula: b b 2 4ac 2a Where the value of b 2 4ac is know as the discriminant. (NOTE: There is a typographical error in the text on pg 185 which lists the discriminant as b 2 4ac ) x The answers may be given in simplified radical form (representing EXACT answers) or may be entered into the calculator and rounded to the nearest hundredth. Use the quadratic formula to solve the following equations. Give both exact answers and rounded decimal values. 1. x2 + 5x – 2 = 0 2. 2x2 + 4x - 7 = 0 3. -2x2 + 7x = 3 4. x2 = 3(x – 2) C. Application: Graphing Quadratic Functions To sketch the graph of a quadratic function that “does not factor”, first determine the vertex using the vertex formula. Then use the quadratic formula to determine exact values for the xintercepts. Convert these values to decimals. Sketch the graph, labeling the vertex and the xintercepts. Example: 1. f(x) = 2x2 + 4x – 7 (see problem B2 on the front.) 2. You Try: f(x) = x2 – 6x + 3 **NOTE: Extra practice on solving all types of Quadratic Equations can be found via the class assignments sheet. Homework: SOLVE THE FOLLOWING PROBLEMS USING THE QUADRATIC FORMULA METHOD (NOT COMPLETING THE SQUARE). GIVE YOUR ANSWERS IN SIMPLIFIED RADICAL FORM. Problems 65 – 71 odd, 75, 77 Also, given the following functions, determine the vertex and x-intercepts to the nearest hundredth and sketch a graph: 1. f(x) = 2x2 – 8x + 1 Worksheet answers: 1) v = (2, -7) Int = .13 and 3.87 2. f(x) = -x2 + 2x + 5 2) v=(1,6) int = -1.45 and 3.45 (054)