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Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation It.

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Presentation on theme: "Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation It."— Presentation transcript:

1 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation It is used primarily for quadratics that CAN NOT be easily factored, but will work with ANY quadratic. I call it the “way that always works”.

2 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation Here is the formula : Just a “heads up” here. It is possible to get answers here that are not integers or fractions. The answers could contain radicals that can not be simplified.

3 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation Here is the formula : Just a “heads up” here. It is possible to get answers here that are not integers or fractions. The answers could contain radicals that can not be simplified. Here is an example :

4 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation Here is the formula : Just a “heads up” here. It is possible to get answers here that are not integers or fractions. The answers could contain radicals that can not be simplified. Here is an example : This could be your answer…

5 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation Here is the formula : Just a “heads up” here. It is possible to get answers here that are not integers or fractions. The answers could contain radicals that can not be simplified. Also, you could get a negative under the radical when evaluating. If that happens, there is no solution because the square root of a negative is not possible.

6 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 1 :Find the solution set for :

7 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 1 :Find the solution set for : a bc a = 1 b = - 1 c = - 6 Substitute these into the formula and then evaluate…

8 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 1 :Find the solution set for : a bc a = 1 b = - 1 c = - 6 Substitute these into the formula and then evaluate…

9 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 1 :Find the solution set for : a bc

10 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 1 :Find the solution set for : a bc

11 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 1 :Find the solution set for : a bc Split your + / -

12 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for :

13 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c a = 3 b = 2 c = - 9 Substitute these into the formula and then evaluate…

14 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c a = 3 b = 2 c = - 9 Substitute these into the formula and then evaluate…

15 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c

16 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c Simplify your radical…

17 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c Simplify your radical…

18 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c Simplify your radical…

19 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c Everything outside the radical is divisible by two…

20 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 2 :Find the solution set for : a b c Answer

21 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 3 :Find the solution set for :

22 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 3 :Find the solution set for : a b c a = 5 b = -1 c = - 3 Substitute these into the formula and then evaluate…

23 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 3 :Find the solution set for : a b c a = 5 b = -1 c = - 3 Substitute these into the formula and then evaluate…

24 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 3 :Find the solution set for : a b c a = 5 b = -1 c = - 3

25 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 3 :Find the solution set for : a b c a = 5 b = -1 c = - 3

26 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 4 :Find the solution set for :

27 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 4 :Find the solution set for : a b c a = 4 b = 3 c = 2 Substitute these into the formula and then evaluate…

28 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 4 :Find the solution set for : a b c a = 4 b = 3 c = 2 Substitute these into the formula and then evaluate…

29 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 4 :Find the solution set for : a b c a = 4 b = 3 c = 2

30 Solving Quadratic Equations – Part 2 Quadratic Formula - another way to solve quadratic equations based on the standard form for a quadratic equation EXAMPLE # 4 :Find the solution set for : a b c a = 4 b = 3 c = 2 NO SOLUTION !!! You have a negative square root…

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