Choose the one alternative that best completes the statement or answers the question.
Determine whether the graph of the parabola opens upward or downward and determine the range.
-$$f ( x ) = - 3 ( x - 2 ) ^ { 2 } - 2$$
A) Downward
Range: $( - \infty , - 2 ]$

B) Upward
Range: $[ - 2 , \infty )$

C) Upward
Range: $[ 2 , \infty )$

D) Downward
Range: $( - \infty , 2 ]$

Question

Choose the one alternative that best completes the statement or answers the question.
Determine whether the graph of the parabola opens upward or downward and determine the range.
-$$f ( x ) = - 3 ( x - 2 ) ^ { 2 } - 2$$
A) Downward
Range: $( - \infty , - 2 ]$

B) Upward
Range: $[ - 2 , \infty )$

C) Upward
Range: $[ 2 , \infty )$

D) Downward
Range: $( - \infty , 2 ]$

Quizplus · Accepted Answer

The coefficient of the squared term is negative (-3), indicating the parabola opens downward. The vertex form of the parabola shows the vertex at (2, -2), making the highest point of the parabola -2. Therefore, the range is all real numbers less than or equal to -2.

Choose the One Alternative That Best Completes the Statement or Answers