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Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.

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Presentation on theme: "Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring."— Presentation transcript:

1 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula

2 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula Let’s look at some simple quadratic equations…

3 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula Let’s look at some simple quadratic equations… EXAMPLE # 1 : To solve these, we will simply take the square root of both sides…

4 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula Let’s look at some simple quadratic equations… EXAMPLE # 1 : To solve these, we will simply take the square root of both sides…

5 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula Let’s look at some simple quadratic equations… EXAMPLE # 1 : All square roots have a positive and negative answer…

6 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula Let’s look at some simple quadratic equations… EXAMPLE # 1 : All square roots have a positive and negative answer…

7 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula Let’s look at some simple quadratic equations… EXAMPLE # 2 : To solve, take the square root of both sides…

8 Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring 3. Using the Quadratic Formula Let’s look at some simple quadratic equations… EXAMPLE # 2 : To solve, take the square root of both sides…

9 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable.

10 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 3 : Find the solution set for

11 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 3 : Find the solution set for This is already in factored form, so we will set the two factors = 0 and solve for “x”… 12

12 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 3 : Find the solution set for This is already in factored form, so we will set the two factors = 0 and solve for “x”… 12

13 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 3 : Find the solution set for This is already in factored form, so we will set the two factors = 0 and solve for “x”… 12

14 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 3 : Find the solution set for This is already in factored form, so we will set the two factors = 0 and solve for “x”… 12 These are our two solutions…

15 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 3 : Find the solution set for This is already in factored form, so we will set the two factors = 0 and solve for “x”… 12 These are our two solutions…solution set is

16 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 4 : Find the solution set for

17 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 4 : Find the solution set for We must start by factoring out the common term “x”…

18 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 4 : Find the solution set for Now set each factor = 0 and solve for “x”…

19 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 4 : Find the solution set for Now set each factor = 0 and solve for “x”… Solution set =

20 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 5 : Find the solution set for

21 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 5 : Find the solution set for Factor difference of squares…

22 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 5 : Find the solution set for Set both factors = 0 and solve for “x”…

23 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 5 : Find the solution set for Set both factors = 0 and solve for “x”… Solution set =

24 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 6 : Find the solution set for

25 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 6 : Find the solution set for Factor trinomial with coefficient = 1

26 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 6 : Find the solution set for Set both factors = 0 and solve for “x”…

27 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 7 : Find the solution set for

28 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 7 : Find the solution set for Factor trinomial with squared coefficient >1

29 Solving Quadratic Equations – Part 1 Factoring – after factoring the equation, we will set each “factor” equal to zero and solve for our variable. EXAMPLE # 7 : Find the solution set for Set both factors = 0 and solve for “x”…

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