Find the range of the quadratic function in interval notation.
-$$f ( x ) = - 2 x ^ { 2 } - 4 x$$
A) $( - \infty , 2 ]$
B) $( - \infty , - 2 ]$
C) $( - \infty , 1 ]$
D) $( - \infty , - 1 ]$

Question

Quizplus · Accepted Answer

The range of a quadratic function is always an interval. The vertex of the parabola is the point where the function changes direction. The x-coordinate of the vertex is $ - \frac { b } { 2 a } $. In this case, $ a = - 2 $ and $ b = - 4 $, so the x-coordinate of the vertex is $ - \frac { - 4 } { 2 ( - 2 ) } = - 1 $. The y-coordinate of the vertex is $ f ( - 1 ) = - 2 ( - 1 ) ^ { 2 } - 4 ( - 1 ) = - 2 + 4 = 2 $. Therefore, the range of the function is $ ( - \infty , 2 ] $.

Find the Range of the Quadratic Function in Interval Notation f(x)=−2x2−4xf ( x ) = - 2 x ^ { 2 } - 4 xf(x)=−2x2−4x

Find the Range of the Quadratic Function in Interval Notation $f ( x ) = - 2 x ^ { 2 } - 4 x$