Topic 4 solving quadratic equations part 1

Solving Quadratic EquationsModule 10 - Topic 4

PART 1

Why do we need to solve Quadratic Equations?

• View this Discovery Education video to see a use for Quadratic Equations AND why math is cool!

http://assignments.discoveryeducation.com/?cdPasscode=T73A6-61BB




• Now, wasn’t that cool? I bet you never look at a pumpkin the same way again!





• Now, wasn’t that cool? I bet you never look at a pumpkin the same way again!

• Let’s look at solving Quadratic Equations a little closer.



What is a Quadratic Equation?• View this Cool Math lesson introducing

Quadratic Equations.

• There are 2 pages of notes.

• Complete the Try It problems in your notebook and check your answers on the next slide.

http://www.coolmath.com/algebra/09-solving-quadratics/01-introduction-01.htm

http://www.coolmath.com/algebra/09-solving-quadratics/01-introduction-01.htm

Page 2 - Try It• Find a, b, and c. !3x2 ! x ! 5 = 0

Page 2 - Try It• Find a, b, and c.

a. -3

b. -1

c. -5

!3x2 ! x ! 5 = 0


a. -3

b. -1

c. -5

• Find a, b, and c.

!3x2 ! x ! 5 = 0

x2 ! 6 = 0


a. -3

b. -1

c. -5

• Find a, b, and c.

a. 1

b. 0 (The x term is missing so b is 0.)

c. -6

!3x2 ! x ! 5 = 0

x2 ! 6 = 0

Solving Quadratic Equations by Factoring

• View this Cool Math website to learn about solving Quadratic Equations.

• There are 9 pages to view.

• Complete the Try It problems in your notebook and check your answers on the next slides.

http://www.coolmath.com/algebra/09-solving-quadratics/02-solving-quadratic-equations-by-factoring-01.htm

http://www.coolmath.com/algebra/09-solving-quadratics/02-solving-quadratic-equations-by-factoring-01.htm

Page 4 - Try It• Solve. x2 + 8x +12 = 0


Factor the trinomial.


x + 6( ) x + 2( ) = 0Factor the trinomial.


x + 6( ) x + 2( ) = 0Factor the trinomial.

Split the factors and set equal to 0.


x + 6( ) x + 2( ) = 0

x + 6 = 0 or x + 2 = 0




x + 6( ) x + 2( ) = 0

x + 6 = 0 or x + 2 = 0



Solve each equation.


x + 6( ) x + 2( ) = 0

x + 6 = 0 or x + 2 = 0!6 !6 !2 !2





x + 6( ) x + 2( ) = 0

x + 6 = 0 or x + 2 = 0!6 !6 !2 !2 x = !6 or x = !2





x + 6( ) x + 2( ) = 0

x + 6 = 0 or x + 2 = 0!6 !6 !2 !2 x = !6 or x = !2




Answer: !6,!2{ }

Page 5 - Try It & Your Turn• Solve:

x2 ! 6x + 9 = 0


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

Answer: 3{ }


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

8x2 ! 26x ! 7 = 0

Answer: 3{ }


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

8x2 ! 26x ! 7 = 0

2x ! 7( ) 4x +1( ) = 0

Answer: 3{ }


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

8x2 ! 26x ! 7 = 0

2x ! 7( ) 4x +1( ) = 02x ! 7 = 0 or 4x +1 = 0

Answer: 3{ }


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

8x2 ! 26x ! 7 = 0

2x ! 7( ) 4x +1( ) = 02x ! 7 = 0 or 4x +1 = 0

+7 +7 !1 !1

Answer: 3{ }


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

8x2 ! 26x ! 7 = 0

2x ! 7( ) 4x +1( ) = 02x ! 7 = 0 or 4x +1 = 0

+7 +7 !1 !1

2x = 7 or 4x = !1

Answer: 3{ }


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

8x2 ! 26x ! 7 = 0

2x ! 7( ) 4x +1( ) = 02x ! 7 = 0 or 4x +1 = 0

+7 +7 !1 !1

x =72

or x = !14

2x = 7 or 4x = !1

Answer: 3{ }


x2 ! 6x + 9 = 0

x ! 3( ) x ! 3( ) = 0x ! 3 = 0 or x ! 3 = 0+3 +3 +3 +3

x = 3 or x = 3

8x2 ! 26x ! 7 = 0

2x ! 7( ) 4x +1( ) = 02x ! 7 = 0 or 4x +1 = 0

+7 +7 !1 !1

x =72

or x = !14

2x = 7 or 4x = !1

Answer: 3{ }Answer: 7

2,! 1

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Page 6 - Your Turn• Solve. 4a2 + 3a = 0


a 4a + 3( ) = 0


a 4a + 3( ) = 0a = 0 or 4a + 3 = 0


a 4a + 3( ) = 0a = 0 or 4a + 3 = 0

!3 !3


a 4a + 3( ) = 0a = 0 or 4a + 3 = 0

!3 !3 4a = !3


a 4a + 3( ) = 0a = 0 or 4a + 3 = 0

!3 !3 4a = !3 4 4


a 4a + 3( ) = 0a = 0 or 4a + 3 = 0

!3 !3 4a = !3

a = !34

4 4


a 4a + 3( ) = 0a = 0 or 4a + 3 = 0

!3 !3 4a = !3

a = !34

4 4

Answer: 0,! 34

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Page 7 - Try It• Solve. x2 ! 25 = 0


x + 5( ) x ! 5( ) = 0


x + 5( ) x ! 5( ) = 0

x + 5 = 0 or x ! 5 = 0


x + 5( ) x ! 5( ) = 0

x + 5 = 0 or x ! 5 = 0!5 !5 +5 +5


x + 5( ) x ! 5( ) = 0

x + 5 = 0 or x ! 5 = 0!5 !5 +5 +5

x = !5 or x = 5


x + 5( ) x ! 5( ) = 0

x + 5 = 0 or x ! 5 = 0!5 !5 +5 +5

x = !5 or x = 5

Answer: !5,5{ }

Page 8 - Try It• Solve. 5x3 ! 45x = 0


5x x2 ! 9( ) = 0


5x x2 ! 9( ) = 05x x + 9( ) x ! 9( ) = 0


5x x2 ! 9( ) = 0

5x = 0 or x + 9 = 0 or x ! 9 = 0

5x x + 9( ) x ! 9( ) = 0


5x x2 ! 9( ) = 0

5x = 0 or x + 9 = 0 or x ! 9 = 0 5 5 !9 !9 +9 +9

5x x + 9( ) x ! 9( ) = 0


5x x2 ! 9( ) = 0

5x = 0 or x + 9 = 0 or x ! 9 = 0 5 5 !9 !9 +9 +9 x = 0 or x = !9 or x = 9

5x x + 9( ) x ! 9( ) = 0


5x x2 ! 9( ) = 0

5x = 0 or x + 9 = 0 or x ! 9 = 0 5 5 !9 !9 +9 +9 x = 0 or x = !9 or x = 9

5x x + 9( ) x ! 9( ) = 0

Answer: 0,!9,9{ }

Page 9 - Your Turn• Solve. 2y3 + 5y2 ! 3y = 0


y 2y2 + 5y ! 3( ) = 0


y 2y2 + 5y ! 3( ) = 0y 2y !1( ) y + 3( ) = 0


y 2y2 + 5y ! 3( ) = 0

y = 0 or 2y !1 = 0 or y + 3 = 0y 2y !1( ) y + 3( ) = 0


y 2y2 + 5y ! 3( ) = 0

y = 0 or 2y !1 = 0 or y + 3 = 0+1 +1 !3 !3

y 2y !1( ) y + 3( ) = 0


y 2y2 + 5y ! 3( ) = 0

y = 0 or 2y !1 = 0 or y + 3 = 0+1 +1 !3 !3 2y = 1 or y = !3

y 2y !1( ) y + 3( ) = 0


y 2y2 + 5y ! 3( ) = 0

y = 0 or 2y !1 = 0 or y + 3 = 0+1 +1 !3 !3 2y = 1 or y = !3

y 2y !1( ) y + 3( ) = 0

2 2


y 2y2 + 5y ! 3( ) = 0

y = 0 or 2y !1 = 0 or y + 3 = 0+1 +1 !3 !3 2y = 1 or y = !3

y 2y !1( ) y + 3( ) = 0

2 2 y = 1

2


y 2y2 + 5y ! 3( ) = 0

y = 0 or 2y !1 = 0 or y + 3 = 0+1 +1 !3 !3 2y = 1 or y = !3

y 2y !1( ) y + 3( ) = 0

2 2 y = 1

2Answer: 0, 12

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Algebra Cruncher• Practice solving more Quadratic Equations at this Cool

Math website.

• Select the “Give me a Problem” button to try new problems.

• Do your work in a notebook before entering your answer.

• When you select “What’s the Answer?” your answer is erased and correct answer is displayed. Having your work in a notebook will allow you to compare your answer to the correct answer.

• Keep working problems until you get 3 in a row correct.

http://www.coolmath.com/crunchers/algebra-problems-solving-quadratics-factoring.htm




Fantastic Job!• You’ve finished reviewing Solving Quadratic

Equations Part 1.

• Exit and proceed to Part 2.

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Topic 4 solving quadratic equations part 1