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Published byBritney Reed Modified over 5 years ago

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Quadratic Formula

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Standard Form of a Quadratic Equation ax 2 + bx + c = 0 example x 2 + 6x + 8 = 0 we learned to solve this by: factoring completing the square now we’ll learn the Quadratic Formula

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x 2 + 6x + 8 = 0 factor x 2 + 6x + 8 = 0 (x + 4 ) (x + 2 ) = 0 x = -4 or x = -2 complete the square x 2 + 6 x + ___ = -8 + ___ 99 ( x + 3 ) 2 = 1 x + 3 = + 1 x = -3 + 1 x = - 3 - 1 x = -2x = - 4

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Quadratic Formula This formula finds the solution(s) for x in any quadratic equation. let’s try it for x 2 + 6x + 8 = 0

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x 2 + 6x + 8 = 0 a = ____ b = ____ c = ____ 1 68 substitute these numbers into the formula = -2 = -4

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x 2 –3x – 10 = 0 = 5= -2 a=___ b=___ c=___ 1 -3 -10

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3x 2 – x = 2 write in standard form 3x 2 – x – 2 = 0 a = ___ b = ____ c = ____3 -2 = 1= - 2/3

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x 2 = x – 8 Write in standard form x 2 – x + 8 = 0a=___ b=__ c=___ 1 8 there is no square root of a negative number No Solution

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8x 2 = 3 write in standard form there is no “x” term 8x 2 –3 = 0 rewrite as : 8x 2 + 0 x – 3 = 0 a = ___ b = ___ c = ___80-3 4

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4x 2 + 12x + 9 = 0 a = ____ b = ____ c = ____ 4129 only one solution

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Deriving the Quadratic Formula ax 2 + bx + c = 0 isolate x’s on one sideax 2 + bx = -c divide each term by a complete the square write as a binomial square find common denominator Given

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isolate the x separate the radical take the square root of both sides simplify the denominator combine the fractions The Quadratic Formula!! combine fractions on the right

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Can you recite the quadratic formula? 2a

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