1. Quadratic Formula
Solving for X
Solving for quadratic equations

2. 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 :

3. The Quadratic Formula.

4. 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.

5. 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.

6. 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 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.

7. 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.

8. 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