1. Revision - Quadratic Equations Solving Quadratic equations by the Quadratic Formula. By I Porter

2. Introduction The complete the square method of solving quadratic equations can be used to derive a formula to solve any quadratic equation. For any quadratic equation ax 2 + bx + c = 0, where a ≠ 0, Proof: (not required for examination) For any quadratic equation ax 2 + bx + c = 0, where a ≠ 0 Divide throughout by ‘a’ Rearrange If the term to complete the square LHS. Factorise LHS Rearrange RHS Take √ of both sides. Rearrange, x =.. Quadratic formula, a ≠0.

3. Example 1: Use the quadratic formula to solve. x 2 + 6x + 8 = 0 Always test on one you can factorise! For ax 2 + bx + c = 0, then a = +1, b = +6, c = +8 Write-out the substitution into formula Evaluate as an exact value! Note: b 2 - 4ac ≥ 0 for ax 2 + bx + c = 0 to have solutions. This is called the discriminant.

4. Example 2: Use the quadratic formula to solve. 3x 2 - 6x + 2 = 0 For ax 2 + bx + c = 0, then a = +3, b = -6, c = +2 Write-out the substitution into formula Evaluate as an exact value! Note: b 2 - 4ac ≥ 0 for ax 2 + bx + c = 0 to have solutions. This is called the discriminant. Reduce all surds.

5. Example 3: Use the quadratic formula to solve. For ax 2 + bx + c = 0, then a = +1, b = -1, c = -1 Write-out the substitution into formula Evaluate as an exact value! Rearrange. You may have to give your answer correct a set number of decimal places or significant figures using your calculator to give an approximation. Correct to 2 decimal places. Quadratic Equation.

6. Exercise: Find exact solution to the following. a) x 2 + 8x - 9 = 0 b) 2x 2 - 6x - 5 = 0 c) 5x 2 - x - 2 = 0 d) 4x 2 - x - 1 = 5x + 4 e)