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icang [17]
3 years ago
6

Question 6(Multiple Choice Worth 1 points)

Mathematics
1 answer:
Alenkinab [10]3 years ago
5 0

Answer:

(-1,-6)

Step-by-step explanation:

We have the following function:

f(x) = x^{2} + 6x + 3

The following transformation is applied

g(x) = f(x - 2)

So

g(x) = f(x - 2) = (x - 2)^{2} + 6(x - 2) + 3

g(x) = x^{2} - 4x + 4 + 6x - 12 + 3

g(x) = x^{2} + 2x - 5

For a second order function in the format:

g(x) = ax^{2} + bx + c

The vertex is:

V = (x_{v}, g(x_{v})

In which

x_{v} = -\frac{b}{2a}

In this problem

a = 1, b = 2

So

x_{v} = -\frac{2}{2*1} = -1

Then

g(x_{v}}) = g(-1) = (-1)^{2} +2(-1) - 5 =  -6

So the correct answer is:

(-1,-6)

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hope this helps! :)

v(x) = 12 - 2x - 5\\v(-2) = 12 - 2(-2) - 5\\v(-2) = 12 + 4 - 5\\v(-2) = 11\\-----------------------------\\v(0) = 12 - 2(0) - 5\\v(0) = 12 - 0 -5\\v(0) = 7\\-----------------------------\\v(5) = 12 - 2(5) - 5\\v(5) = 12 - 10 - 5\\v(5) = -3

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