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What is the answer for question 2) ? http://postimg.org/image/behx7ffhr/ (Reminder) :...

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jayson94 | Salutatorian

Posted August 3, 2013 at 7:49 PM via web

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What is the answer for question 2) ?

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted August 3, 2013 at 9:22 PM (Answer #1)

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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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