WRITING QUADRATIC FUNCTIONS IN STANDARD FORM WORKSHEET

In each case, write the given quadratic function in standard form :

Problem 1 :

f(x) = x² - 4x + 5

Problem 2 :

f(x) = x² + 8x - 10

Problem 3 :

f(x) = x² - 7x - 8 

Problem 4 :

f(x) = x² + 12x

Problem 5 :

f(x) = 2x² + 8x + 3

Problem 6 :

f(x) = -4x² + 20x - 1

Answers

1. Answer :

f(x) = x² - 4x + 5

f(x) = x² - 2(x)(2) + 5

f(x) = x² - 2(x)(2) + 2² - 2² + 5

f(x) = (x - 2)² - 2² + 5

f(x) = (x - 2)² - 4 + 5

f(x) = (x - 2)² + 1

2. Answer :

f(x) = x² + 8x - 10

f(x) = x² + 2(x)(4) + 4² - 4² + 10

f(x) = (x + 4)² - 4² + 10

f(x) = (x + 4)² - 16 + 10

f(x) = (x + 4)² - 6

3. Answer :

f(x) = x² - 7x - 8

4. Answer :

f(x) = x² + 12x

f(x) = x² + 2(x)(6)

f(x) = x² + 2(x)(6) + 6² - 6²

f(x) = (x + 6)² - 6²

f(x) = (x + 6)² - 36

5. Answer :

f(x) = 2x² + 8x + 3

f(x) = 2(x² + 4x) + 3

f(x) = 2[x² + 2(x)(2) + 2² - 2²] + 3

f(x) = 2[(x + 2)² - 2²] + 3

f(x) = 2[(x + 2)² - 4] + 3

f(x) = 2(x + 2)² - 8 + 3

f(x) = 2(x + 2)² - 5

6. Answer :

f(x) = -4x² + 20x - 1

f(x) = -4(x² - 5x) - 1

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