Question

the function g(x) = 3x2 − 12x 7 written in vertex form is g(x) = 3(x − 2)2 − 5. what is the vertex of g(x)? a.(−6, −5) b.(−2, −5) c.(2, −5) d.(6, −5)

Answer 1

Hello,
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Answer C
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g(x)=3x²-12x+7=3(x²-2*2x+4)+7-12
=3(x-2)²-5
Vertex is (2,-5)
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Answer 2

we know that

The equation of the vertical parabola is of the form

$y=a(x-h)^{2} +k$

where

$(h,k)$ is the vertex of the parabola

In this problem we have

$g(x)=3(x-2)^{2} -5$

The parabola open upward

The vertex is a minimum

The vertex is the point $(2,-5)$

therefore

the answer is the option C

$(2,-5)$