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Write the quadratic function f(x) = 3x2 - 6x + 9 in vertex form. A) f(x) = 3(x - 3)2 + 9 B) f(x) = 3(x - 1)2 + 6 C) f(x) = 3(x + 3)2 + 6 D) f(x) = 3(x + 1)2 + 9

User Hungerstar
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1 Answer

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Answer:

Option B
f(x)=3(x-1)^(2)+6

Explanation:

we have


f(x)=3x^(2) -6x+9

Group terms that contain the same variable, and move the constant to the opposite side of the equation


f(x)-9=3x^(2) -6x

Factor the leading coefficient


f(x)-9=3(x^(2) -2x)

Complete the square. Remember to balance the equation by adding the same constants to each side


f(x)-9+3=3(x^(2) -2x+1)


f(x)-6=3(x^(2) -2x+1)

Rewrite as perfect squares


f(x)-6=3(x-1)^(2)


f(x)=3(x-1)^(2)+6 ------> equation in vertex form

the vertex is the point
(1,6)

User Sdwilsh
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