Identify the vertex and determine the minimum or maximum value of the function.
-$$f ( x ) = - 2 x ^ { 2 } + 8 x - 2$$
A) Vertex: $( 2 , - 6 )$
Minimum: $- 6$

B) Vertex: $( 2,6 )$
Minimum: 6

C) Vertex: $( 2,6 )$
Maximum: 6

D) Vertex: $( 2 , - 6 )$
Maximum: -6

Question

Identify the vertex and determine the minimum or maximum value of the function.
-$$f ( x ) = - 2 x ^ { 2 } + 8 x - 2$$
A) Vertex: $( 2 , - 6 )$
Minimum: $- 6$

B) Vertex: $( 2,6 )$
Minimum: 6

C) Vertex: $( 2,6 )$
Maximum: 6

D) Vertex: $( 2 , - 6 )$
Maximum: -6

Quizplus · Accepted Answer

The vertex of a parabola given by $f(x) = ax^2 + bx + c$ can be found using the formula $x = -\frac{b}{2a}$. For $f(x) = -2x^2 + 8x - 2$, $a = -2$ and $b = 8$, so the x-coordinate of the vertex is $x = -\frac{8}{2(-2)} = 2$. Plugging $x = 2$ back into the function gives $f(2) = -2(2)^2 + 8(2) - 2 = -8 + 16 - 2 = 6$, so the vertex is $(2, 6)$. Since $a = -2 < 0$, the parabola opens downwards, indicating the vertex is a maximum point. Therefore, the maximum value of the function is 6.

Identify the Vertex and Determine the Minimum or Maximum Value f(x)=−2x2+8x−2f ( x ) = - 2 x ^ { 2 } + 8 x - 2f(x)=−2x2+8x−2

Identify the Vertex and Determine the Minimum or Maximum Value $f ( x ) = - 2 x ^ { 2 } + 8 x - 2$