Quadratic Formula

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

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 x + ___ = -8 + ___ 99 ( x + 3 ) 2 = 1 x + 3 = + 1 x = x = x = -2x = - 4

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

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

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

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

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

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

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

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

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

Can you recite the quadratic formula? 2a