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What is the vertex of g(x)=3x^2-12x+7

What is the vertex of g(x)=3x^2-12x+7-example-1
User Hholtij
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2 Answers

5 votes


\large\underline{\mathbb{SOLUTION:}}

Given:


\bm{g(x)=3x^2-12x+7}

To find:


\small\tt{The \: vertex \: of \: the \: parabola.}

We use the Quadratic Function to solve the vertex:


\boxed{ \tt{ y =ax {}^(2) + bx + c } }


\boxed{\tt{x_(v) = - (b)/(2a)}}

Let's compare the coefficients to get:


\longrightarrow \tt{ g(x) = 3 {x }^(2) - 12x + 7}


\purple{\tt{a=3, \: b=-12, \: and \: c=7}}


\longrightarrow\tt{x_(v) = - (b)/(2a ) = - ( ( - 12))/(2(3)) = (12)/(6) = 2 }


\large{\boxed{\purple{\tt{x=2}}}}


\therefore The coordinate of the vertex is
\rm{x=2}.


\qquad \qquad{ \overline{ \qquad \qquad \qquad \qquad \qquad}}

Substitute in the expression of g(x) to get the corresponding y value as follows:


\longrightarrow\tt{ g(x) = 3(2 {)}^(2) - 12(2) + 7}


\longrightarrow\tt{ = 12 - 24 + 7}


\large{\boxed{\purple{\tt{y=-5}}}}


\therefore The coordinate of the vertex is
\rm{y=-5}


\large{\boxed{\rm{The \: vertex \: is \: (2,\: -5)}}}


\large\underline{\mathbb{ANSWER:}}


\tt{(6, \: -5) }


\tt{(-2, \: -5) }


\large{\tt{ \purple{ \large{(2, \: -5)}}}}


\tt{(-6, \: -5) }

What is the vertex of g(x)=3x^2-12x+7-example-1
User Legends
by
7.7k points
5 votes

Answer:

vertex = (2, - 5 )

Explanation:

given a quadratic function

g(x) = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is


x_(vertex) = -
(b)/(2a)

given

g(x) = 3x² - 12x + 7

with a = 3 , b = - 12 , then


x_(vertex) = -
(-12)/(2(3)) = -
(-12)/(6) = - (- 2) = 2

to find the y- coordinate , evaluate g(2)

g(2) = 3(2)² - 12(2) + 7 = 3(4) - 24 + 7 = 12 - 17 = - 5

vertex = (2, - 5 )

User Sebastian Thees
by
8.1k points

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