What is the answer for question 2) ?

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The vertex form of a quadratic is y = a(x - h)^2 + k, where (h, k) is the vertex.

f(x) = x^2 + 8x - 3

y = x^2 + 8x - 3

y + 3 = x^2 + 8x

y + 3 = 1(x^2 + 8x)

y + 3 + 1(16) = 1(x^2 + 8x + 16)

y + 19 = 1(x + 4)^2

y = 1(x + 4)^2 - 19**vertex = (-4, -19)**

f(x) = x^2 - 5x + 8

y = x^2 - 5x + 8

y - 8 = x^2 - 5x

y - 8 = 1(x^2 - 5x)

y - 8 + 1(6.25) = 1(x^2 - 5x + 6.25)

y - 1.75 = 1(x - 2.5)^2

y = 1(x - 2.5)^2 + 1.75**vertex = (2.5, 1.75)**

f(x) = 2x^2 - 12x + 1

y = 2x^2 - 12x + 1

y - 1 = 2x^2 - 12x

y - 1 = 2(x^2 - 6x)

y - 1 + 2(9) = 2(x^2 - 6x + 9)

y + 17 = 2(x - 3)^2

y = 2(x - 3)^2 - 17 **vertex = (3, -17)**

f(x) = 3x^2 + 2x - 5

y = 3x^2 + 2x - 5

y + 5 = 3x^2 + 2x

y + 5 = 3(x^2 + 2x)

y + 5 + 3(1/9) = 3(x^2 + 2/3x + 1/9)

y + 16/3 = 3(x + 1/3)^2

y = 3(x + 1/3)^2 - 16/3 **vertex = (-1/3, -16/3)**

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