2. Why do we need to solve
Quadratic Equations?
β’ 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?
β’ View this Discovery Education video to see a
use for Quadratic Equations AND why math is
cool!
β’ Now, wasnβt that cool? I bet you never look at
a pumpkin the same way again!
4. Why do we need to solve
Quadratic Equations?
β’ View this Discovery Education video to see a
use for Quadratic Equations AND why math is
cool!
β’ Now, wasnβt that cool? I bet you never look at
a pumpkin the same way again!
β’ Letβs look at solving Quadratic Equations a
little closer.
5. What is a Quadratic Equation?
β’ View this Cool Math lesson introducing
Quadratic Equations.
β’ There are 2 pages of notes.
β’ Complete the Try It problems in your notebook
and check your answers on the next slide.
7. Page 2 - Try It
2
β’ Find a, b, and c. β3x β x β 5 = 0
8. Page 2 - Try It
2
β’ Find a, b, and c. β3x β x β 5 = 0
a. -3
b. -1
c. -5
9. Page 2 - Try It
2
β’ Find a, b, and c. β3x β x β 5 = 0
a. -3
b. -1
c. -5
2
β’ Find a, b, and c. x β6=0
10. Page 2 - Try It
2
β’ Find a, b, and c. β3x β x β 5 = 0
a. -3
b. -1
c. -5
2
β’ Find a, b, and c. x β6=0
a. 1
b. 0 (The x term is missing so b is 0.)
c. -6
11. Solving Quadratic Equations by
Factoring
β’ View this Cool Math website to learn about
solving Quadratic Equations.
β’ There are 9 pages to view.
β’ Complete the Try It problems in your notebook
and check your answers on the next slides.
13. Page 4 - Try It
β’ Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
14. Page 4 - Try It
β’ Solve. 2
x + 8x + 12 = 0
Factor the trinomial.
( x + 6 )( x + 2 ) = 0
15. Page 4 - Try It
β’ 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
β’ 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
β’ 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
β’ 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 β6 β6 β2 β2
equation.
19. Page 4 - Try It
β’ 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 β6 β6 β2 β2
equation. x = β6 or x = β2
20. Page 4 - Try It
β’ 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 β6 β6 β2 β2
equation. x = β6 or x = β2
Answer: {β6, β2}
21. Page 5 - Try It & Your Turn
β’ Solve:
2
x β 6x + 9 = 0
22. Page 5 - Try It & Your Turn
β’ Solve:
2
x β 6x + 9 = 0
( x β 3) ( x β 3) = 0
23. Page 5 - Try It & Your Turn
β’ Solve:
2
x β 6x + 9 = 0
( x β 3) ( x β 3) = 0
xβ3= 0 or x β 3 = 0
24. Page 5 - Try It & Your Turn
β’ Solve:
2
x β 6x + 9 = 0
( x β 3) ( x β 3) = 0
xβ3= 0 or x β 3 = 0
+3 +3 +3 +3
25. Page 5 - Try It & Your Turn
β’ Solve:
2
x β 6x + 9 = 0
( x β 3) ( x β 3) = 0
xβ3= 0 or x β 3 = 0
+3 +3 +3 +3
x=3 or x=3
26. Page 5 - Try It & Your Turn
β’ Solve:
2
x β 6x + 9 = 0
( x β 3) ( x β 3) = 0
xβ3= 0 or x β 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
27. Page 5 - Try It & Your Turn
β’ Solve: 2
8x β 26x β 7 = 0
2
x β 6x + 9 = 0
( x β 3) ( x β 3) = 0
xβ3= 0 or x β 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
28. Page 5 - Try It & Your Turn
β’ Solve: 2
8x β 26x β 7 = 0
2
x β 6x + 9 = 0
( 2x β 7 ) ( 4x + 1) = 0
( x β 3) ( x β 3) = 0
xβ3= 0 or x β 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
29. Page 5 - Try It & Your Turn
β’ Solve: 2
8x β 26x β 7 = 0
2
x β 6x + 9 = 0
( 2x β 7 ) ( 4x + 1) = 0
( x β 3) ( x β 3) = 0
2x β 7 = 0 or 4x + 1 = 0
xβ3= 0 or x β 3 = 0
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
30. Page 5 - Try It & Your Turn
β’ Solve: 2
8x β 26x β 7 = 0
2
x β 6x + 9 = 0
( 2x β 7 ) ( 4x + 1) = 0
( x β 3) ( x β 3) = 0
2x β 7 = 0 or 4x + 1 = 0
xβ3= 0 or x β 3 = 0 +7 +7 β1 β1
+3 +3 +3 +3
x=3 or x=3
Answer: {3}
31. Page 5 - Try It & Your Turn
β’ Solve: 2
8x β 26x β 7 = 0
2
x β 6x + 9 = 0
( 2x β 7 ) ( 4x + 1) = 0
( x β 3) ( x β 3) = 0
2x β 7 = 0 or 4x + 1 = 0
xβ3= 0 or x β 3 = 0 +7 +7 β1 β1
+3 +3 +3 +3 2x = 7 or 4x = β1
x=3 or x=3
Answer: {3}
32. Page 5 - Try It & Your Turn
β’ Solve: 2
8x β 26x β 7 = 0
2
x β 6x + 9 = 0
( 2x β 7 ) ( 4x + 1) = 0
( x β 3) ( x β 3) = 0
2x β 7 = 0 or 4x + 1 = 0
xβ3= 0 or x β 3 = 0 +7 +7 β1 β1
+3 +3 +3 +3 2x = 7 or 4x = β1
x=3 or x=3 7 1
x= or x=β
2 4
Answer: {3}
64. Algebra Cruncher
β’ Practice solving more Quadratic Equations at this Cool
Math website.
β’ Select the βGive me a Problemβ button to try new
problems.
β’ Do your work in a notebook before entering your answer.
β’ When you select βWhatβs the Answer?β 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.
β’ Keep working problems until you get 3 in a row correct.
65. Fantastic Job!
β’ Youβve ο¬nished reviewing Solving Quadratic
Equations Part 1.
β’ Exit and proceed to Part 2.