Identify the vertex and determine the minimum or maximum value of the function.
-$$f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$$
A) Vertex: $( 4,7 )$
Maximum: 7

B) Vertex: $( 4,7 )$
Minimum: 7

C) Vertex: $( 4 , - 7 )$
Minimum: -7

D) Vertex: $( 4 , - 7 )$
Maximum: -7

Question

Identify the vertex and determine the minimum or maximum value of the function.
-$$f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$$
A) Vertex: $( 4,7 )$
Maximum: 7

B) Vertex: $( 4,7 )$
Minimum: 7

C) Vertex: $( 4 , - 7 )$
Minimum: -7

D) Vertex: $( 4 , - 7 )$
Maximum: -7

Quizplus · Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function, $h = 4$ and $k = 7$, so the vertex is $(4, 7)$. Since $a = -2$ is negative, the parabola opens downwards, indicating a maximum value at the vertex. Thus, the maximum value is 7.

Identify the Vertex and Determine the Minimum or Maximum Value f(x)=−2(x−4)2+7f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7f(x)=−2(x−4)2+7

Identify the Vertex and Determine the Minimum or Maximum Value $f ( x ) = - 2 ( x - 4 ) ^ { 2 } + 7$