Verified answer

a) f(x) = x² - 6x + 5

x² - 6x + 5 = 0

(- b/2a)² = (- 6/(2 * 1))² = (- 6/2)² = (36/4) = 9

x² - 6x + 9 = - 5 + 9

(x - 3)² = 4

√(x - 3)² = √4

x - 3 = ± 2

x' = 2 + 3 = 5

x'' = - 2 + 3 = 1

b) f(x) = x² + 10x + 21

x² + 10x + 21 = 0

(- b/2a)² = (- 10/(2 * 1))² = (- 10/2)² = (100/4) = 25

x² + 10x + 25 = - 21 + 25

(x + 5)² = 4

√(x + 5)² = √4

x + 5 = ± 2

x' = 2 - 5 = - 3

x'' = - 2 - 5 = - 7

c) f(x) = x² - 2x - 3

x² - 2x - 3 = 0

(- b/2a)² = (- 2/(2 * 1))² = (- 2/2)² = (4/4) = 1

x² - 2x + 1 = 3 + 1

(x - 1)² = 4

√(x - 1) = √4

x - 1 = ± 2

x' = 2 + 1 = 3

x'' = - 2 + 1 = - 1

d) f(x) = x² + 4x + 3

x² + 4x + 3 = 0

(- b/2a)² = (- 4/(2 * 1))² = (- 4/2)² = (16/4) = 4

x² + 4x + 4 = - 3 + 4

(x + 2)² = 1

√(x + 2)² = √1

x + 2 = ± 1

x' = 1 - 2 = - 1

x'' = - 1 - 3 = - 4

e) f(x) = x² - 8x + 12

x² - 8x + 12 = 0

(- b/2a)² = (- (- 8)/(2 * 1))² = (8/2)² = (64/4) = 16

x² - 8x + 16 = - 12 + 16

(x - 4)² = 4

√(x - 4)² = √4

x - 4 = ± 2

x' = 2 + 4 = 6

x'' = - 2 + 4 = 2

f) f(x) = 3x² - 8x - 3

3x² - 8x - 3 = 0

x² - (8x/3) - 1 = 0 (complemento do quadrado a = 1)

(- b/2a)² = [(- 8/3)/(2 * 1)]² = [(- 8/3)/2]² = (8/6)² = (4/3)² = 16/9

x² - (8x/3) + 16/9 = 1 + 16/9

(x - 4/3)² = 25/9

√(x - 4/3)² = √(25/9)

x - 4/3 = ± 5/3

x' = 5/3 + 4/3 = 9/3 = 3

x'' = - 5/3 + 4/3 = - 1/3

x^2 - 6x + 5 = 0

x^2 - 6x = -5

x^2 - 6x + 9 = -5 + 9

(x - 3)^2 = 4

x - 3 = raiz(4) --> x = 3 + 2 = 5

x - 3 = - raiz(4) --> x = 3 - 2 = 1

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x^2 + 10 + 21 = 0

x^2 + 10x = -21

x^2 + 10x + 25 = -21 + 25

(x + 5)^2 = 4

x + 5 = raiz(4) --> x = 2 - 5 = -3

x + 5 = -raiz(4) --> x = -2 - 5 = -7

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