Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = - 5 x ^ { 2 } - 10 x$$
A) minimum at $( 1 , - 5 )$
B) maximum at $( 1 , - 5 )$
C) maximum at $( - 1,5 )$
D) minimum at $( - 1,5 )$

Question

Quizplus · Accepted Answer

The quadratic function $f(x) = -5x^2 - 10x$ is a downward-opening parabola (since the coefficient of $x^2$ is negative), indicating a maximum value. The vertex form of a parabola $ax^2 + bx + c$ gives the vertex at $x = -\frac{b}{2a}$. Here, $a = -5$ and $b = -10$, so $x = -\frac{-10}{2(-5)} = -1$. Substituting $x = -1$ into the function gives $f(-1) = -5(-1)^2 - 10(-1) = 5$. Thus, the maximum is at $(-1, 5)$.

Use the Quadratic Function to Determine If the Function Has f(x)=−5x2−10xf ( x ) = - 5 x ^ { 2 } - 10 xf(x)=−5x2−10x

Use the Quadratic Function to Determine If the Function Has $f ( x ) = - 5 x ^ { 2 } - 10 x$