Find the maximum or minimum value of the function. Approximate to two decimal places.
-$f ( x ) = - 8.4 x ^ { 2 } - 1.9 x - 9.3$
A) $2.03$
B) $- 9.19$
C) $- 9.62$
D) $- 0.11$

Question

Quizplus · Accepted Answer

The function $f(x) = -8.4x^2 - 1.9x - 9.3$ is a quadratic function in the form of $ax^2 + bx + c$, where $a = -8.4$, $b = -1.9$, and $c = -9.3$. Since $a < 0$, the parabola opens downwards, indicating that the vertex of the parabola represents the maximum value of the function. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$. Substituting the values of $a$ and $b$, we get:$$x = -\frac{-1.9}{2(-8.4)} = \frac{1.9}{16.8}$$Plugging this $x$ value back into the original equation gives the maximum value of the function. Calculating this value accurately will yield a result close to $-9.19$, making option B the correct answer.

Find the Maximum or Minimum Value of the Function f(x)=−8.4x2−1.9x−9.3f ( x ) = - 8.4 x ^ { 2 } - 1.9 x - 9.3f(x)=−8.4x2−1.9x−9.3

Find the Maximum or Minimum Value of the Function $f ( x ) = - 8.4 x ^ { 2 } - 1.9 x - 9.3$