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**10-7 The Quadratic Formula**

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**What Does The Formula Do ?**

The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factor. The formula states that for a quadratic equation of the form : ax2 + bx + c = 0 The roots of the quadratic equation are given by :

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Example 1 Use the quadratic formula to solve the equation : x 2 + 5x + 6= 0 Solution: x 2 + 5x + 6= 0 a = 1 b = 5 c = 6 x = - 2 or x = - 3 These are the roots of the equation.

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Example 2 Use the quadratic formula to solve the equation : 8x 2 + 2x - 3= 0 Solution: 8x 2 + 2x - 3= 0 a = 8 b = 2 c = -3 x = ½ or x = - ¾ These are the roots of the equation.

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Example 3 Use the quadratic formula to solve the equation : 8x x + 15= 0 Solution: 8x x + 15= 0 a = 8 b = c = 15 x = 3/2 or x = 5/4 These are the roots of the equation.

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Example 4 Use the quadratic formula to solve for x to 2 d.p : 2x 2 +3x - 7= 0 Solution: 2x 2 + 3x – 7 = 0 a = 2 b = 3 c = - 7 x = or x = These are the roots of the equation.

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Warm Up 1.) Write 15x 2 + 6x = 14x 2 -12 in standard form. (ax 2 + bx + c = 0) 2.) Evaluate b 2 – 4ac when a = 3, b = -6, and c = 5.

Warm Up 1.) Write 15x 2 + 6x = 14x 2 -12 in standard form. (ax 2 + bx + c = 0) 2.) Evaluate b 2 – 4ac when a = 3, b = -6, and c = 5.

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