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5191125-29527500Notes #4 – Solving Quadratic Equations SOL A.4cWarm Up:12 = 22 = 32 =42 =52 =62 =72 =82 =92 =102 =Some quadratic equations are very easy to solve for x. Just get x by itself!1. x2 = 252. 3x2 = 48 3. 2x2 + 5 = 23Other times, it is not as easy to get x by itself. For example: x2 = 6x – 8 52387506921500There are two ways we can find solutions to these problems, by graphing and by factoring. Both have the same FIRST step.Step 1: _______________________________________________________________so that your equation now looks like: ____________________________.Graphing MethodFactoring MethodStep 1: Get all terms to one side (ax2 + bx + c = 0)Step 1: Get all terms to one side (ax2 + bx + c = 0)Step 2: Graph the function.Step 2: Factor the trinomial.Step 3: Locate the roots (x-intercepts) on your graph.Step 3: Set each factor equal to zero and solve.Final Answer: Can have no roots, 1 root, or 2 rootsFinal Answer: Can have no roots, 1 root, or 2 roots5313188-22860000Example #1: Solve the following quadratic equation x2 = -4x – 3 Graphing MethodFactor Method-1047751504950039147756032500Example #2: Solve the following quadratic equation 3x2 + x = 4 Graphing MethodFactor Method-10477517462500507682528575000You try! Solve the quadratic equation either by using the graphing method or the factoring method.n2 + 7n + 15 = 54. 7x2 + 2x = 037719002476500-952524765001943100306716007r2 ? 14r = ?75. x2 ? 11x + 24 = 036195006032500142875603250050768255524500n2 + 8n = ?156. x2 + 3x = -236195001911350014287511493500 ................
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