Write the function in vertex form and determine the range.
-$$f ( x ) = - 3 x ^ { 2 } + 18 x - 33$$
A) $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$

B) $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$

C) $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$

D) $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$

Question

Write the function in vertex form and determine the range.
-$$f ( x ) = - 3 x ^ { 2 } + 18 x - 33$$
A) $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$

B) $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$

C) $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$

D) $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$

Quizplus · Accepted Answer

The vertex form of the given quadratic function is obtained by completing the square, and the range is determined by the direction of the parabola (downward, since the coefficient of $x^2$ is negative) and the vertex's y-coordinate.

Write the Function in Vertex Form and Determine the Range f(x)=−3x2+18x−33f ( x ) = - 3 x ^ { 2 } + 18 x - 33f(x)=−3x2+18x−33

Write the Function in Vertex Form and Determine the Range $f ( x ) = - 3 x ^ { 2 } + 18 x - 33$