standard form: sf: sf: sf: sf · go to butenhoffmath.com and check out the algebra notes video: a...

Go to butenhoffmath.com and check out the algebra notes video: A 8-1 AStd5a: I can rewrite quadratic equations in standard form, factored form, and vertex form. Factored form: y = (x + 2)(x +3)

FF: y = (2x +3)(x − 4)

FF: y = (x − 6)2

FF:

Vertex Form: y = (x + 5)2 + 2

−2x −30

x2 15x

Standard form:

SF: SF: SF: SF:

A 8-1 Name_________________________________BDFM?________Why?_________________________________ AStd5a: I can rewrite quadratic equations in standard form, factored form, and vertex form. 1. Factored form: y = (x + 6)(x + 7)

FF: y = (x +8)(x + 9)

FF: y = (4x +1)(x + 2)

Are the two forms of the quadratic equivalent? Justify your answer. y = (x −3)(x −10) and y = x2 −13x +30

Standard form: SF: SF:

2. Write one complete sentence describing what the factored form of a quadratic looks like. 3. Factored form: y = (x +1)(x − 5)

FF: y = (x − 5)(x + 6)

FF: y = (2x − 5)(x + 9)

Are the two forms of the quadratic equivalent? Justify your answer. y = (x − 5)(2x +1) and y = 2x2 −11x − 5

Standard form:

SF:

SF:

4. Write one complete sentence describing what the standard form of a quadratic looks like. 5. Factored form: y = (x +1)2

FF: y = (x − 5)2

FF: y = (2x + 6)2

Are the two forms of the quadratic equivalent? Justify your answer. y = (x − 5)2 and y = 2x2 −10x + 25

Standard form: SF: SF:

6. Factored form: Standard form:

2x 4

x2 2x

FF: SF:

3x 9

x2 3x

FF: SF:

−9x 81

x2 −9x

FF: SF:

−7x 49

x2 −7x

FF: SF:

2x 6

x2 3x

FF: SF:

2x 14

x2 7x

FF: SF:

3x −18

x2 −6x

FF: SF:

8x −72

x2 −9x

7. Vertex form: y = (x + 2)2 + 5

VF: y = (x + 4)2 − 7

VF: y = (x − 7)2 +1

Are the two forms of the quadratic equivalent? Justify your answer. y = (x + 4)2 − 5 and y = x2 +8x + 9

Standard form:

SF: SF:

8. Write one complete sentence describing what the vertex form looks like. 9. FF: SF:

x 5

2x2 10x

FF: SF:

3x 12

2x2 8x

FF: SF:

−x −3

2x2 6x

FF: SF:

12x −20

3x2 −5x

Go to butenhoffmath.com and check out the algebra notes video: A 8-2 AStd5a: I can rewrite quadratic equations in factored form given the standard form. Step 1 x2 +8x + 7

Step 2 x2 +8x + 7

Step 3

Step 4 x2 +8x + 7 =

Step 1

Step 2 Step 3 Step 4

1. What are the factors of 12? 2. x2 + 7x +12=

3. x2 +8x +12=

4. x2 +13x +12=

A 8-2 Name__________________________________________BDFM?_________Why?_______________________ AStd5a: I can rewrite quadratic equations in factored form given the standard form. 1. What are the factors of 16? 2. x2 +8x +16=

3. x2 +10x +16=

4. x2 +17x +16 =

5. What are the factors of 20? 6. x2 + 9x + 20=

7. x2 +12x + 20=

8. x2 + 21x + 20=

9. What are the factors of 18? 10. x2 + 9x +18=

11. x2 +11x +18=

12. x2 +19x +18=

13. What are the factors of 24? 14. 24252 ++ xx =

15. 24142 ++ xx =

16. 24112 ++ xx =

17. 24102 ++ xx =

18. 24232 −+ xx =

19. 24102 −+ xx =

21. 2452 −+ xx =

22. 2422 −+ xx =

23. 24232 −− xx =

24. 24102 −− xx =

25. 2452 −− xx =

26. 2422 −− xx =

27. Write an equation in the given form. a. Linear

b. Factored form c. Standard form d. Vertex form

Are the following pairs of quadratic equations equivalent? Justify your answer. 28. y = (x −3)(x + 4) and

y = x2 + 7x −12

29. y = (x − 6)2 and y = x2 +36

30. y = (x + 4)2 − 5 and y = x2 +8x +16

31. Find the factored form and the standard form. FF: SF:

−x −4

3x2 12x

FF: SF:

−3x −6

2x2 4x

FF: SF:

−2x 8

3x2 −12x

FF: SF:

−5x 20

2x2 −8x

Go to butenhoffmath.com and check out the algebra notes video: A 8-3 AStd5a: I can rewrite quadratic equations in vertex form given the standard form by completing the perfect square.

Vertex form: y = (x +3)2 − 4

Convert this equation to standard form.

Fill in the blank to complete the perfect square and write the factored/vertex form. x2 +12x + _____ x2 +14x + _____

Standard Form: y = x2 +12x + 7

Convert this equation to vertex form.

Standard Form: y = x2 +14x −10


A 8-3 Name________________________________BDFM?_______Why?___________________________________ AStd5a: I can rewrite quadratic equations in vertex form given the standard form by completing the perfect square. 1. Fill in the blank to complete the perfect square and write the factored/vertex form x2 +18x + _____

x2 + 2x + _____

x2 − 6x + _____

x2 +8x + _____

x2 + 24x + _____

x2 + 9x + _____

2. Find the vertex form by completing the perfect square.

Standard Form: y = x2 +18x +3


Standard Form: y = x2 + 2x + 5


Standard Form: y = x2 − 6x −1


Standard Form: y = x2 +8x +10


Standard Form: y = x2 + 24x − 5


Standard Form: y = x2 + 9x + 2


3. Find all the factors of 5. 4. Find the factored form.

a. y = x2 + 6x + 5

b. y = x2 + 4x − 5 c. y = x

2 − 6x + 5 d. y = x2 − 4x − 5

5. Find the factored form (FF) and the standard form (SF). FF: SF:

2x 8

3x2 12x

FF: SF:

5x 30

2x2 12x

FF: SF:

15x −20

3x2 −4x

FF: SF:

3x −18

2x2 −12x

6. Are the quadratic equations equivalent? Show by completing the square. y = x2 +8x + 25

and y = (x + 4)2 +10

y = x2 −10x + 26

and y = (x − 5)2 +1

y = x2 +8x +16 and y = (x + 4)2 +1

7. Convert y = x2 + 6x +8 to standard form, factored form and vertex form.

Theresa wanted to solve −2 2x2 + x −10( )2= x − 2( )2

and she knows that her final equation has to be set equal to zero. Here are her first two steps:

−2 2x2 + x −10( )2= x − 2( )2

4 2x2 + x −10( ) = x2 − 4x + 4

8. Help her finish rewriting the quadratic in standard form.

Go to butenhoffmath.com and check out the algebra notes video: A 8-4 AStd5a: I can rewrite quadratic equations in factored form given the standard form. Step 1 3x2 + 7x + 2

Step 2 3x2 + 7x + 2

Step 3

Step 4 3x2 + 7x + 2

Step 1

Step 2 Step 3 Step 4

Factor. 1. 3x2 + 4x +1=

2. 3x2 +10x +3 =

3. 3x2 +13x + 4 =

A 8-4 Name_____________________________BDFM?_________Why?____________________________________ AStd5a: I can rewrite quadratic equations in factored form given the standard form. Factor. 1. 2x2 +3x +1=

2. 2x2 + 5x + 2 =

3. 2x2 + 7x +3 =

4. 2x2 + 9x + 4 =

5. 2x2 +11x + 5=

6. 2x2 + 4x + 2 =

7. 2x2 + 5x +3=

8. 2x2 + 6x + 4 =

9. 2x2 +13x + 6 =

10. 2x2 −13x + 6 =

11. 2x2 −11x − 6 =

12. 2x2 +11x − 6 =

Multiply

13. 2(x2 + 6x + 9)

14. 4(x2 − x − 6) 15. 5(x2 + 2x −15)

Factor out.

16. 2x2 +12x +18

17. 4x2 − 4x − 24 18. 5x2 +10x − 75

19. 2x2 + 24x + 22

20. 2x2 −16x +14 21. 3x2 − 9x −30

22. Refer back to #19. a. Find the factored form of #19 before you factored out.

b. Find the factored form of #19 after you factored out.





25. Without factoringhich quadratic expressions below may have more than one factored form? Explain your reasoning.

a. 3x2 −18x + 27

b. x2 −11x +111 c. −4x2 −12x −8 d. 3x2 +3x −12

A 8-Review Name______________________________BDFM?________Why?_______________________________ 1. Write one complete sentence that describes what you learned this chapter. C-Level Find the standard form 2. Factored form: y = (x + 6)(x + 7)

3. Factored form: y = (x − 5)(x + 6)

4. Vertex form: y = (x + 2)2 + 5

5. Vertex form: y = (x − 7)2 +1

Find the factored form. 6. y = x2 +14x + 24

7. y = x2 − 7x −8

B-Level Find the standard form. Find the factored form. 8. Factored form:

)7)(62( ++= xxy

9. Factored form: )6)(53( +−= xxy

10. Standard form: y = 2x2 + 7x +3

11. Standard form: y = 3x2 + x − 2

12. Find the vertex form. y = x2 + 6x +18

Are the two forms of the quadratic equivalent? Justify your answer. 13. y = (x +3)2 and y = x2 + 9

14. y = (x + 4)2 − 5 and y = x2 +8x + 9

Find the standard form. A-Level 15. Factor out a number to simplify 3x2 +18x +15

16. Refer to #15. Find the factored form before you factored out and then find the factored form after you factored out.

17. Without factoring, which quadratic expressions below may have more than one factored form? Explain your reasoning.

a. 3x2 −18x + 27

b. x2 −11x +111 c. −4x2 −12x −8 d. 3x2 +3x −12

Theresa wanted to solve −2 5x2 + 2x −3( )2= x + 5( )2

and she knows that her final equation has to be set equal to zero. Here are her first two steps:

−2 5x2 + 2x −3( )2= x + 5( )2

4 5x2 + 2x −3( ) = x2 + 5x + 25

18. Help her finish rewriting the quadratic in standard form.

standard form: sf: sf: sf: sf · go to butenhoffmath.com and check out the algebra notes video: a...

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