11

Algebra 2: Section 5.6Algebra 2: Section 5.6

The Quadratic Formula The Quadratic Formula & the Discriminant& the Discriminant

22

The Quadratic FormulaThe Quadratic Formula

2

2

0 :

4

2

The solutions of

ax bx c are

b b acx

a

33

ExamplesExamples21. 3 8 35x x

23 8 35 0x x 3; 8; 35a b c

28 8 4(3)( 35)

2(3)x

Have to write in standard form first!

2 4

2

b b acx

a

44

28 8 4(3)( 35)

2(3)x

8 64 420

6x

8 484

6x

8 22

6x

55

8 22 8 22 or

6 6x x

8 22

6x

14 30 or

6 6x x

7 or 5

3x x

66

ExamplesExamples22. 12 5 2 13x x

22 12 18 0x x 2; 12; 18a b c

212 ( 12) 4(2)(18)

2(2)x

2 4

2

b b acx

a

77

12 144 144

4x

12 0

4x

12

4x

212 ( 12) 4(2)(18)

2(2)x

3x

88

ExamplesExamples23. -2 2 3x x

22 2 3 0x x 2; 2; 3a b c

22 ( 2) 4(2)(3)

2(2)x

2 4

2

b b acx

a

99

2 4 24

4x

2 20

4x

2 2 5

4

ix

22 ( 2) 4(2)(3)

2(2)x

1010

2 2 5

4 4

ix

2 2 5

4

ix

1 5

2 2

ix

Split them up!!!

Sometimes one will simplify and the other won’t!

1111

HomeworkHomework

p.295 p.295 #17-29 first column#17-29 first column

#33-43 odds #33-43 odds

ADD YOUR HOMEWORK FOR ADD YOUR HOMEWORK FOR TODAY TO YESTERDAY’S!!!TODAY TO YESTERDAY’S!!!

1212

1313

Algebra 2: Section 5.6Algebra 2: Section 5.6

The Quadratic Formula & The Quadratic Formula & the Discriminantthe Discriminant

(Day 2)(Day 2)

1414

The DiscriminantThe Discriminant

The expression The expression underunder the radical the radical in the quadratic formulain the quadratic formula

2 4b ac

2 4

2

b b acx

a

1515

The DiscriminantThe Discriminant

If discriminant is If discriminant is positivepositive–Two real solutionsTwo real solutions

If discriminant is If discriminant is zerozero–One real solutionOne real solution

If discriminant is If discriminant is negativenegative–Two imaginary solutionsTwo imaginary solutions

1616

ExamplesExamples

Use the discriminant to determine the number Use the discriminant to determine the number and type of solutions of the equation.and type of solutions of the equation.

21. 9 6 1 0x x 9; 6; 1a b c

26 4(9)(1)

2 4b ac

36 36 One real solution0

1717

ExamplesExamples22. 9 6 4 0x x 9; 6; 4a b c

26 4(9)( 4)

2 4b ac

36 144

Two real solutions

180

1818

ExamplesExamples23. 9 6 5 0x x 9; 6; 5a b c

26 4(9)(5)

2 4b ac

36 180

Two imaginary solutions

144

1919

HomeworkHomework

p.296 p.296 #46-67 all#46-67 all

Look at 46 – 55……Look at 46 – 55……