Quadratic Formula Solving for X Solving for quadratic equations.

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Presentation transcript:

Quadratic Formula Solving for X Solving for quadratic equations

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 factorise. The formula states that for a quadratic equation of the form : ax2 + bx + c = 0 The roots of the quadratic equation are given by :

The Quadratic Formula.

x 2 + 5x + 6= 0 a = 1 b = 5 c = 6 x = - 2 or x = - 3 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.

x = ½ or x = - ¾ 8x 2 + 2x - 3= 0 a = 8 b = 2 c = -3 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.

x = 3/2 or x = 5/4 8x 2 - 22x + 15= 0 a = 8 b = -22 c = 15 Example 3 Use the quadratic formula to solve the equation : 8x 2 - 22x + 15= 0 Solution: 8x 2 - 22x + 15= 0 a = 8 b = -22 c = 15 x = 3/2 or x = 5/4 These are the roots of the equation.

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 These are the roots of the equation.

CLASSWORK 1. a2 – 4a + 16 2. x2 + 8x + 12 3. y2 + 4y + 4 4. 9y2 + 4y + 5 5. 3r2 – r + 27 6. a2 + 10a - 8