CONVERTING FROM THREE DIFFERENT FORMS OF QUADRATIC FUNCTIONS WORKSHEET

Converting From Standard Form

Convert the quadratic function from standard form to

i) Vertex form

ii) Factored form

Problem 1 :

y = x2 - 8x + 15

Solution

Problem 2 :

y = x2 - 4x

Solution

Problem 3 :

y = x2 + 4x + 3

Solution

Problem 4 :

y = 3x2 - 6x + 3

Solution

Problem 5 :

y = x2 + 6x + 5

Solution

Answer Key


1)

2)

3)

4)

5)

Vertex form

y = (x - 4)2 - 1

y = (x - 2)2 - 4

y = (x + 2)2 - 1

y = 3(x - 1)2 + 0

y = (x + 3)2 - 4

Factored form

y = (x - 3) (x - 5)

y = x(x - 4)

y = (x + 1) (x + 3)

y = 3(x - 1)(x - 1)

y = (x + 1) (x + 5)

Converting From Factored Form

Convert the quadratic function from factored to

i) Standard form

ii) Vertex form

Problem 6 :

y = (x + 4)(x + 3)

Solution

Problem 7 :

y = -2(x + 2)(x - 1)

Solution

Problem 8 :

y = 3(2x - 1)(x - 1)

Solution

Problem 9 :

y = (5x + 1)(x - 3)

Solution

Problem 10 :

y = (x - 10)(x - 6)

Solution

Answer Key

6)  

Standard Form:

y = x2 + 7x + 12

Vertex Form:

y = (x + 7/2)2 - 1/4

7)  

Standard Form:

y = -2x2 - x + 4

Vertex Form:

y = -2(x + 1/4)2 + 33/8

8)  

Standard Form:

y = 6x2 - 9x + 3

Vertex Form:

y = 6(x - 3/4)2 - 3/8

Standard Form:

y = 5x2 - 14x - 3

Vertex Form:

y = 5(x - 7/5)2 - 64/5

10) 

Standard Form:

y = x2 - 16x + 60

Vertex Form:

y = (x - 8)2 - 4

Converting From Vertex Form

Convert the quadratic function from vertex form to

i) Standard form

ii) Factored form

Problem 11 :

y = (x - 4)2 - 9

Solution

Problem 12 :

y = (x + 2)2 - 9

Solution

Problem 13 :

y=x+722-14

Solution

Problem 14 :

y=6x-342-38

Solution

Problem 15 :

y =5x-752- 645

Solution

Answer Key

11)

Standard Form:

y = x2 - 8x + 7

Factored Form:

y = (x - 1) (x - 7)

12)

Standard Form:

y = x2 + 4x - 5

Factored Form:

y = (x - 1) (x + 5)

13)

Standard Form:

y = x2 + 7x + 12

Factored Form:

y = (x + 4)(x + 3)

14)

Standard Form:

y = 6x2 - 9x + 3

Factored Form:

y = 3(2x - 1) (x - 1)

15)

Standard Form:

y = 5x2 - 14x - 3

Factored Form:

y = (5x + 1) (x - 3)

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