1. Solving Quadratic Equations Cont’d.

2. To Solve A Quadratic Equation When b = 0… Use the same procedures you used to solve an equation to get the “x” isolated (by itself). Instead of having an “x” left, you have an “x²”. When the “x²” is isolated, find the square root of both sides (be sure to give both the principal and the negative roots!).

3. Example 1 Solve:2x² - 18 = 0 Add 18 to both sides2x² = 18 Divide both sides by 2x² = 9 Find the square root of both sides x = ± 3

4. Example 2 Solve:2x² + 72 = 0 Subtract 72 from both sides 2x² = -72 Divide both sides by 2x² = -36 Find the square root of both sides— oops!! You can’t find the square root of a negative number (-36) so there is NO SOLUTION!

5. Try these… 4x 2 + 1 = 17 Find the radius of a circle whose area is 125 in 2. 81x 2 - 49 = 0 3x 2 – 85 = 2x 2 – 36 4x 2 + 72 = 2x 2 - 28

6. The Quadratic Formula

7. The Discriminant This is the part of the equation under the radical sign. (b 2 – 4ac) When that is positive, there will be two answers. When that is negative, there will be no real solution. When that is zero, there will be one answer.

8. Find the number of solutions: 2x 2 + 4x + 3 = 0 a = 2; b = 4; c = 3 b 2 – 4ac (4) 2 – (4)(2)(3) 16 – 24= -8 The answer is negative, so there are no real solutions.

9. Find the number of solutions: 2x 2 – 11x + 6 = 0 a = 2; b = -11; c = 6 b 2 – 4ac (-11) 2 – (4)(2)(6) 121 – 48= 73 The answer is positive, so there are two real solutions.

10. Find the number of solutions: 2x 2 + 12x = -18 2x 2 + 12x + 18 = 0 a = 2; b = 12; c = 18 b 2 – 4ac (12) 2 – (4)(2)(18) 144 – 1444= 0 The answer is zero, so there is one real solution.

11. Try these… 3x + 2x 2 + 6 = 0 3x 2 = 13x – 4 9x 2 + 16 = -24x

12. Quadratic Formula

13. 6x 2 + 7x – 5 = 0 a = 6, b = 7, c = -5

14. 5x 2 – 4x = 33 -33 -33 5x 2 – 4x – 33 = 0 a = 5, b = -4, c = -33

15. 6x 2 – 150 = 0 Since b = 0, I would use the square root method. Add 130 to both sides 6x 2 = 150 Divide both sides by 6 x 2 = 25 Find the square root of both sides and round to the nearest hundredth. x = 5, and –5

16. Try these… x 2 + x – 12 = 0 2x 2 + x – 7 = 0