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Anvisha [2.4K]
3 years ago
14

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
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
8 0

Answer:

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

Step-by-step 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)

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