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# Download Section 3.2a - Solving Quadratic Equations by Factoring

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MAC 1105 Section 3.2a – Solving Quadratic Equations by Factoring A quadratic equation – one that contains an x2 term – can be solved by setting the equation = 0, factoring, then setting EACH factor = 0, and solving the new equation(s). When factoring, remember to ask yourself: A. Can I take anything out? 1. 5x2 – 6x = 0 2. 7x2 – 21x = 0 B. Is it the difference of two squares? 3. 4x2 – 25 = 0 4. 144x2 – 49 = 0 C. Is it a trinomial? 5. x2 - 7x - 8 = 0 6. x2 +12x – 36 = 0 7. 2x2 + 11x – 6 = 0 D. Have I factored completely? 8. x3 - 6x2 - 27x = 0 9. –2x2 + 32 = 0 E. If the equation if not "=0" you must FIRST simplify and get 0 on one side, with the polynomial in descending order. Remember to get rid of parentheses and denominators before adding or subtracting. 10. 6x - 27 = 3x2 - 12x 11. 2 2 x x 2x 3 3 F. Shortcut for binomials – isolate the x2 term and square root both sides. Remember to use 12. x2 – 7 = 0 13. 9x2 – 11 = 0 G. Applications: In graphing quadratic functions it is helpful to identify both the vertex AND the xintercepts. To find the x-intercepts of any function we substitute 0 for y and solve for x. b b Determine the vertex , f and x-intercepts of the following quadratic functions, and 2a 2a sketch the graphs. 1. f(x) = -3x2 + 12 2. f(x) = 3x(x – 4) – 15 Homework: Problems 1 – 7, 13, 21, and part c only of problems 31, 33, 35, 45, 47, 53 In addition, work the following two problems: Determine the vertex and x-intercepts and sketch the graph (no calculators): 1. f(x) = x2 + 4x – 32 2. f(x) = -2x2 + 18 Selected Answers: 2) 3, 6 4) 0, 7 6) -7, -1/4 Worksheet answers: 1) V = (-2, -36) Int: -8 and 4 2) V = (0, 18) Int: 3 and -3 054