Quadratic Formula

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Quadratic Formula

  1. 1. Solving Quadratic Equations using the Quadratic Formula General equation of a quadratic: ax 2 bx c 0 Quadratic Formula: x b b2 2a 4ac Page 3 You must get equation equal to zero before you determine a,b, and c. Notice where the letters come from for the formula We use the quadratic formula when something can not be factored. However, it also works for factorable quadratic equations as well.
  2. 2. #10: x 2 8 x 13 0 a 1 b 8 x b2 2a b c 13 8 x 8 21 x 12 Before you can find a,b, and c, you must get equation = to 0. 4 3 x 2 3 x 2 4ac 12 2 Simplify the radical 8 2 3 2 4 Type what is under the radical exactly as written on your calculator. 4 1 13 8 Page 3 Divide by the denominator, if you can 3 Roots:
  3. 3. a 3 b 0 c b2 2a b x 5 0 43 23 0 x 4 15 2 15 x 5 60 6 x Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form. 4ac 2 0 x 60 Page 3 3x 2 5 0 #14: 2 15 6 15 3 Simplify the radical Divide by the denominator, if you can. Since I can’t, divide by GCF Roots:
  4. 4. #16: x 2 a 1 b 12 x c b2 2a b 29 12 x 12 28 2 x 8.64 x 8.6 12 Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth. 4ac 12 21 x x Page 3 12 x 29 0 2 4 1 29 Since we are solving to the nearest tenth, we do not need to simplify the radical! 28 2 x 12 28 2 x 3.35 x 3.4 Be careful when typing this into your calculator. I recommend that you type in the numerator then hit enter, then divide by denominator! Roots:
  5. 5. x 2 8 10 x 10x 10x #25: x 2 Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth. 10x 8 0 a 1 b 10 b x c 8 10 x x Page 3 10 2 b2 2a 4ac 2 10 21 10 68 x 2 68 10 x x 9.12 x 9.1 41 8 68 2 x .87 x .9 Roots:
  6. 6. 3x x 2 #25: 1 Page 3 3x 2 6 x 1 1 1 Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth. 3x 2 6 x 1 0 a b c x 3 6 b2 2a b x 4ac x 1 6 x 6 23 6 2 43 1 6 48 x 6 x 2.15 x 2.1 Roots 48 6 x x 48 6 6 .15 .2
  7. 7. #25: 2x2 a b 2x2 1 4x 4x 4x 4x 1 0 8 Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form. 2 4 x b2 2a b c 1 x Page 3 4 4 2 2 2 4 22 x x 2 4ac x 42 1 4 2 2 2 Roots: 8 4 4 2 2 4 Divide by the denominator, if you can. Since I can’t, divide by GCF

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