2. 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!
3. 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!
• Now, wasn’t that cool? I bet you never look at
a pumpkin the same way again!
4. 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!
• 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.
5. 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.
7. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0
8. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0
a. -3
b. -1
c. -5
9. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0
a. -3
b. -1
c. -5
2
• Find a, b, and c. x −6=0
10. Page 2 - Try It
2
• Find a, b, and c. −3x − x − 5 = 0
a. -3
b. -1
c. -5
2
• Find a, b, and c. x −6=0
a. 1
b. 0 (The x term is missing so b is 0.)
c. -6
11. 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.
13. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
14. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
15. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0.
16. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
17. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each
equation.
18. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each −6 −6 −2 −2
equation.
19. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each −6 −6 −2 −2
equation. x = −6 or x = −2
20. Page 4 - Try It
• Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
Split the factors
and set equal to 0. x+6=0 or x+2=0
Solve each −6 −6 −2 −2
equation. x = −6 or x = −2
Answer: {−6, −2}
21. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
22. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
23. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
24. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
25. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
26. Page 5 - Try It & Your Turn
• Solve:
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
27. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
28. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
29. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
30. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
31. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3 2x = 7 or 4x = −1
x=3 or x=3
Answer: {3}
32. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3 2x = 7 or 4x = −1
x=3 or x=3 7 1
x= or x=−
2 4
Answer: {3}
33. Page 5 - Try It & Your Turn
• Solve: 2
8x − 26x − 7 = 0
2
x − 6x + 9 = 0
( 2x − 7 ) ( 4x + 1) = 0
( x − 3) ( x − 3) = 0
2x − 7 = 0 or 4x + 1 = 0
x−3= 0 or x − 3 = 0 +7 +7 −1 −1
+3 +3 +3 +3 2x = 7 or 4x = −1
x=3 or x=3 7 1
x= or x=−
2 4
Answer: {3} ⎧ 7 1 ⎫
Answer: ⎨ , − ⎬
⎩ 2 4 ⎭
57. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
58. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
59. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
60. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3
61. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3
2 2
62. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3
2 2
y= 1
2
63. Page 9 - Your Turn
3 2
• Solve. 2y + 5y − 3y = 0
( 2
y 2y + 5y − 3 = 0 )
y ( 2y − 1) ( y + 3) = 0
y=0 or 2y − 1 = 0 or y+3= 0
+1 +1 −3 −3
2y = 1 or y = −3
2 2
⎧ 1 ⎫ y= 1
2
Answer: ⎨0, , −3⎬
⎩ 2 ⎭
64. 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.
65. Fantastic Job!
• You’ve finished reviewing Solving Quadratic
Equations Part 1.
• Exit and proceed to Part 2.